Method for generating a composite glyph and rendering a region of the composite glyph in object-order

ABSTRACT

A method renders a region of a composite glyph. The composite glyph is defined by a set of elements. A set of two-dimensional distance fields is generated using the set of elements, where each two-dimensional distance field is partitioned into cells and each cell includes a method for reconstructing the corresponding two-dimensional distance field within the cell. A composition of the set of two-dimensional distance fields represents the composite glyph. The region of the composite glyph is then rendered using the set of two-dimensional distance fields.

RELATED APPLICATION

This application is a Continuation in Part of a U.S. patent applicationtitled “Method for Antialiasing an Object Represented as aTwo-Dimensional Distance Field in Object-Order,” Ser. No. 10/396,861,filed on Mar. 25, 2003 by Frisken, et al.

FIELD OF THE INVENTION

The invention relates generally to the field of computer graphics, andmore particularly to generating and rendering objects represented bytwo-dimensional distance fields.

BACKGROUND OF THE INVENTION

In the field of computer graphics, the rendering of two-dimensionalobjects is of fundamental importance. Two-dimensional objects, such ascharacter shapes, corporate logos, and elements of an illustrationcontained in a document, are rendered as static images or as a sequenceof frames comprising an animation. There are numerous representationsfor two-dimensional objects and it is often the case that onerepresentation is better than another representation for specificoperations such as rendering and editing. In these cases, a conversionfrom one form to another is performed.

Although we focus here on digital type, possibly the most common andimportant two-dimensional object, the following discussion applies toall types of two-dimensional objects.

We begin with some basic background on digital type. A typical Latinfont family, such as Times New Roman or Arial, includes a set of fonts,e.g., regular, italic, bold and bold italic. Each font includes a set ofindividual character shapes called glyphs. Each glyph is distinguishedby its various design features, such as underlying geometry, strokethickness, serifs, joinery, placement and number of contours, ratio ofthin-to-thick strokes, and size.

There are a number of ways to represent fonts, including bitmaps,outlines, e.g., Type 1 [Adobe Systems, Inc. 1990] and TrueType [AppleComputer, Inc. 1990], and procedural fonts, e.g., Knuth's Metafont, withoutlines being predominant. Outline-based representations have beenadopted and popularized by Bitstream Inc. of Cambridge, Mass., AdobeSystems, Inc. of Mountain View, Calif., Apple Computer, Inc., ofCupertino, Calif., Microsoft Corporation of Bellevue, Wash., URW ofHamburg, Germany, and Agfa Compugraphic of Wilmington, Mass.

Hersch, “Visual and Technical Aspects of Type,” Cambridge UniversityPress. 1993 and Knuth, ‘TEX and METAFONT: New Directions inTypesetting,” Digital Press, Bedford, Mass. 1979, contain comprehensivereviews of the history and science of fonts.

Of particular importance are two classes of type size: body type sizeand display type size. Fonts in body type are rendered at relativelysmall point sizes, e.g., 14 pt. or less, and are used in the body of adocument, as in this paragraph. Body type requires high qualityrendering for legibility and reading comfort. The size, typeface, andbaseline orientation of body type rarely change within a singledocument.

Fonts in display type are rendered at relatively large point sizes,e.g., 36 pt. or higher, and are used for titles, headlines, and indesign and advertising to set a mood or to focus attention. In contrastto body type, the emphasis in display type is on esthetics, where thelack of spatial and temporal aliasing is important, rather thanlegibility, where contrast may be more important than antialiasing. Itis crucial that a framework for representing and rendering type handlesboth of these classes with conflicting requirements well.

Type can be rendered to an output device, e.g., printer or display, asbi-level, grayscale, or colored. Some rendering engines use bi-levelrendering for very small type sizes to achieve better contrast. However,well-hinted grayscale fonts can be just as legible.

Hints are a set of rules or procedures stored with each glyph to specifyhow an outline of the glyph should be modified during rendering topreserve features such as symmetry, stroke weight, and a uniformappearance across all the glyphs in a typeface.

While there have been attempts to design automated and semi-automatedhinting systems, the hinting process remains a major bottleneck in thedesign of new fonts and in the tuning of existing fonts forlow-resolution display devices. In addition, the complexity ofinterpreting hinting rules precludes the use of hardware for fontrendering. The lack of hardware support forces compromises to be madeduring software rasterization, such as the use of fewer samples perpixel and poor filtering methods, particularly when animating type inreal time.

Grayscale font rendering typically involves some form of antialiasing.Antialiasing is a process that smoothes out jagged edges or staircaseeffects that appear in bi-level fonts. Although many font renderingengines are proprietary, most use supersampling, after grid fitting andhinting, with 4 or 16 samples per pixel followed by down-sampling with a2×2 or 4×4 box filter, respectively.

Rudimentary filtering, such as box filtering, is justified by the needfor rendering speed. However, even that approach is often too slow forreal-time rendering, as required for animated type, and the renderedglyphs suffer from spatial and temporal aliasing.

Three important trends in typography reveal some inherent limitations ofprior art font representations and associated methods and thus providethe need for change.

The first trend is the increasing emphasis of reading text on-screen dueto the dominant role of computers in the office, the rise in popularityof Internet browsing at home, and the proliferation of PDAs and otherhand-held electronic devices. These displays typically have a resolutionof 72–150 dots per inch, which is significantly lower than theresolution of printing devices.

This low-resolution mandates special treatment when rasterizing type toensure reading comfort and legibility, as evidenced by the resourcesthat companies such as Microsoft and Bitstream have invested in theirrespective ClearType and Font Fusion technologies.

The second trend is the use of animated type, or kinetic typography.Animated type is used to convey emotion, to add interest, and tovisually attract the reader's attention. The importance of animated typeis demonstrated by its wide use in television and Internet advertising.

The third trend is the proliferation of display devices that incorporatenumerous layouts for components of pixels of such displays. Verticallyand horizontally striped RGB components have been the standardarrangement for conventional displays, as described in U.S. Pat. No.6,188,385 “Method and apparatus for displaying images such as text”,Hill et al. Arranging the components differently, however, has numerousadvantages, as described in U.S. Patent Application publication number20030085906 “Methods and systems for sub-pixel rendering using adaptivefiltering”, Elliott et al.

Unfortunately, traditional outline-based fonts and corresponding methodshave limitations in all of these areas. Rendering type on alow-resolution display requires careful treatment in order to balancethe needs of good contrast for legibility, and reduced spatial and/ortemporal aliasing for reading comfort.

As stated above, outline-based fonts are typically hinted to provideinstructions to the rendering engine for optimal appearance. Fonthinting is labor intensive and expensive. For example, developing awell-hinted typeface for Japanese or Chinese fonts, which can have morethan ten thousand glyphs, can take years. Because the focus of hintingis on improving the rendering quality of body type, the hints tend to beineffective for type placed along arbitrary paths and for animated type.

Although high quality filtering can be used to antialias grayscale typein static documents that have a limited number of font sizes andtypefaces, the use of filtering in animated type is typically limited byreal-time rendering requirements.

Prior art sub-pixel rendering methods, like those described in U.S. Pat.No. 6,188,385, have numerous disadvantages pertaining to all threetrends.

First, they require many samples per pixel component to get adequatequality, which is inefficient. When rendering on alternative pixellayouts comprising many components, e.g., such as the layouts describedin U.S. Patent Application publication number 20030085906, their methodsbecome impractical. Second, they exploit the vertical or horizontalstriping of a display to enable reuse of samples for neighboring pixelcomponents, which fails to work with many alternative pixel componentlayouts. Third, they use a poor filter when sampling each componentbecause of the inefficiencies of their methods when using a betterfilter.

Fourth, the methods taught do not provide any measure for mitigatingcolor fringing on alternative pixel component layouts. Fifth,translations of a glyph by non-integer pixel intervals requirere-rendering of the glyph. Re-rendering usually requires re-interpretinghints, which is inefficient. Sixth, hints are often specific to aparticular pixel component layout, and therefore must be redone tohandle the proliferation of alternative pixel component layouts. Redoinghints is both expensive and time consuming.

Rendering Overlapping Objects

When two or more objects are rendered, their rendered images mayoverlap. For example, the antialiased edges of two glyphs in a line oftext may overlap when the glyphs are placed close together. As anotherexample, a single Kanji glyph may be represented by a composition ofseveral elements, such as strokes, radicals, or stroke-based radicals,which may overlap when they are combined to render the single Kanjiglyph.

In such cases, a rendering method must handle a region where the objectsoverlap. There are several methods in the prior art for handling suchoverlap regions. The “Painter's Algorithm” is a common approach used incomputer graphics for two-dimensional and three-dimensional rendering.In the Painter's Algorithm, objects are ordered back-to-front and thenrendered in that order. Pixels determined by each rendering simplyoverwrite corresponding pixels in previous renderings.

Other prior art methods blend color or intensity values of overlappingpixels, i.e., those methods combine the color or intensity valuesaccording to a rule, such as choosing a maximum or a minimum value orperforming an arithmetic average of the overlapping pixels. Some ofthose methods use alpha values associated with each pixel to blend thevalues of the overlapping pixels using a technique called alphablending.

Those prior art methods can be problematic for a number of reasons.

For example, the Painter's Algorithm results in color artifacts betweenclosely spaced glyphs when rendering on liquid crystal displays (LCDs),organic light emitting diodes (OLEDs), or similar display technologieswith separately addressable pixel components.

Prior art methods that blend pixel colors or intensities requireadditional computation and storage for alpha values and exhibit variousartifacts such as edge blurring or edge dropout depending on theblending method used.

In addition, coverage values determined for a set of overlapping objectsusing prior art coverage-based antialiasing cannot, in general, beblended together to represent the actual coverage of the combinedobject.

Another prior art approach for handling overlapping objects combines theobjects to produce a composite object prior to rendering. For example,for an outline-based glyph composed of multiple elements, the outlinesof the elements are joined to form a single outline description prior torendering. Similarly, for rendering a stroke-based glyph composed ofmultiple strokes, the strokes are combined into a single set of strokesbefore rendering.

For object elements represented as distance fields, the distance fieldscan be combined into a single distance field prior to rendering usingCSG operations as described by Perry et al., “Kizamu: A System forSculpting Digital Characters,” Proceedings ACM SIGGRAPH 2001, pp. 47–56,2001. When the composite object is represented as an adaptively sampleddistance field, the composite object can require significantly morestorage than the total storage required by the elements because thecombining may introduce fine detail such as very thin sections orcorners into the composite object that are not present in any element.

All of those prior art methods that combine prior to rendering requireadditional storage space and complex operations to generate thecomposite object. Furthermore, those methods require two passes, one tobuild the composite object and one to render the composite object.

Generating and Rendering Component-Based Glyphs

An Asian font, such as a Chinese, Japanese, or Korean font, can include10,000 or more glyphs. In order to reduce memory requirements, glyphs insuch fonts can be represented as compositions of a common set ofcomponents, herein referred to as elements, such as strokes or radicals.These common elements are then stored in a memory as a font library andcombined either prior to rendering or during rendering to produce acomposite glyph.

Prior art methods define the elements using outline descriptors,typically Bezier curves, or stroked skeletons. The elements can becombined prior to rendering into a single shape descriptor, such as acombined outline or a combined set of strokes. Alternatively, eachelement can be rendered independently, producing, for each pixel, eitherantialiased intensities or coverage values from the elements that arecombined to produce a final antialiased intensity or coverage value forthe pixel. Both approaches have problems as described above.

SUMMARY OF THE INVENTION

The invention provides a method to render a composite glyph. Thecomposite glyph is defined by a set of elements. A set oftwo-dimensional distance fields is generated using the set of elements,where each two-dimensional distance field is partitioned into cells andeach cell includes a method for reconstructing the correspondingtwo-dimensional distance field within the cell. A composition of the setof two-dimensional distance fields represents the composite glyph. Theregion of the composite glyph is then rendered using the set oftwo-dimensional distance fields.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1A and 1B are block diagrams of prior art distance fieldrepresentations for glyphs;

FIG. 2A and 2B are block diagrams of distance field representationsaccording to a preferred embodiment of the invention;

FIG. 3 is a block diagram of a bi-quadratic cell of the distance fieldaccording to a preferred embodiment of the invention;

FIG. 4 is a flow diagram of a method for antialiasing an object inimage-order according to the invention;

FIG. 5 is a graph of a linear filter used by the invention;

FIGS. 6A, 6B, and 6C are diagrams of samples near a component of apixel;

FIG. 7 is a flow diagram of a method for antialiasing an object inobject-order according to the invention;

FIG. 8 is a flow diagram of a method for distance-based automatichinting according to the invention;

FIG. 9 is a flow diagram of a method for converting a pen stroke to adistance field according to the invention;

FIG. 10 is a flow diagram of a method for converting a two-dimensionalobject to a distance field according to the invention;

FIG. 11 is a flow diagram of a method for converting a distance field toboundary descriptors according to the invention;

FIG. 12 is a flow diagram of a method for animating an object accordingto the invention;

FIG. 13 is a flow diagram of a method for generating a two-dimensionaldistance field within a cell enclosing a corner of a two-dimensionalobject according to the invention;

FIG. 14 is a flow diagram of a method for antialiasing a set of objectsin image-order according to the invention;

FIG. 15 is a flow diagram of a method for antialiasing a set of objectsin object-order according to the invention;

FIG. 16 is a flow diagram of a method for rendering cell-based distancefields using texture mapping according to the invention;

FIG. 17 is a flow diagram of a method for rendering according to theinvention;

FIG. 18 is a flow diagram of a method for typesetting a set of glyphsaccording to the invention;

FIG. 19 is a flow diagram of a method for generating a composite glyphand rendering a region of the composite glyph in image-order accordingto the invention;

FIG. 20 is a flow diagram of a method for generating a composite glyphand rendering a region of the composite glyph in object-order accordingto the invention;

FIGS. 21A–21D is a diagram of a corner cell according to the invention;

FIGS. 22A–22C is a diagram of a two-segment cell according to theinvention;

FIG. 23 is a flow diagram of a method for generating a two-dimensionaldistance field within a cell associated with a two-dimensional objectaccording to the invention;

FIG. 24A is a diagram of a portion of an object within a region;

FIGS. 24B–24D is a diagram of three configurations of cells partitioninga region according to the invention; and

FIG. 25 is a flow diagram of a method for generating an optimalconfiguration of a distance field for a region of a shape descriptorrepresenting an object according to the invention.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT

Distance Field Representation of Glyphs

Our invention represents a closed two-dimensional shape S, such as aglyph, a corporate logo, or any digitized representation of an object,as a two-dimensional signed distance field D. For the purpose of ourdescription, we use glyphs.

Informally, the distance field of a glyph measures a distance, e.g., aminimum distance, from any point in the field to the edge of the glyph,where the sign of the distance is negative if the point is outside theglyph and positive if the point is inside the glyph. Points on the edgehave a zero distance.

Formally, the distance field is a mapping

for all p ε

such that D(p)=sign(p)·min{∥p−q∥: for all points q on the zero-valuediso-surface, i.e., edge, of S}, sign(p)={−1 if p is outside S, +1 if pis inside S}, and ∥·∥ is the Euclidean norm.

Prior art coverage-based rendering methods that use a single discretesample for each pixel or for each pixel component can completely missthe glyph even when the sample is arbitrarily close to the outline. Therendered glyph has jagged edges and dropout, which are both forms ofspatial aliasing. If the glyph is animated, then temporal aliasingcauses flickering outlines and jagged edges that seem to ‘crawl’ duringmotion. Taking additional samples per pixel or per pixel component toproduce an antialiased rendition can reduce these aliasing effects, butmany samples may be required for acceptable results.

In contrast, continuously sampled distance values according to ourinvention indicate a proximity of the glyph, even when the samples areoutside the shape, thereby eliminating the dropout artifacts of theprior art. The continuous nature of the sampled distance values can beused, according to our invention, to mitigate spatial aliasingartifacts.

Furthermore, because the distance field varies smoothly, i.e., it is C⁰continuous, sampled values change slowly as the glyph moves, reducingtemporal aliasing artifacts.

Distance fields have other advantages. Because they are an implicitrepresentation, they share the benefits of implicit functions. Inparticular, distance fields enable an intuitive interface for designingfonts. For example, individual components of glyphs such as stems, bars,rounds, and serifs can be designed separately. After design, thecomponents can be blended together using implicit blending methods tocompose different glyphs of the same typeface.

Distance fields also have much to offer in the area of kinetictypography or animated type because distance fields provide informationimportant for simulating interactions between objects.

In a preferred embodiment, we use adaptively sample distance fields,i.e., ADFs, see U.S. Pat. No. 6,396,492, “Detail-directed hierarchicaldistance fields,” Frisken, Perry, and Jones, incorporated herein byreference.

ADFs are efficient digital representations of distance fields. ADFs usedetail-directed sampling to reduce the number of samples required torepresent the field. The samples are stored in a spatial hierarchy ofcells, e.g., a quadtree, for efficient processing. In addition, ADFsprovide a method for reconstructing the distance field from the sampledvalues.

Detail-directed or adaptive sampling samples the distance fieldaccording to a local variance in the field: more samples are used whenthe local variance is high, and fewer samples are used when the localvariance is low. Adaptive sampling significantly reduces memoryrequirements over both regularly sampled distance fields, which sampleat a uniform rate throughout the field, and 3-color quadtrees, whichalways sample at a maximum rate near edges.

FIGS. 1A–1B compare the number of cells required for a 3-color quadtreefor a Times Roman ‘a’ and ‘D’ with the number of cells required for abi-quadratic ADF in FIGS. 2A–2B of the same accuracy. The number ofcells is directly related to storage requirements. Both quadtrees have aresolution equivalent to a 512×512 image of distance values. The 3-colorquadtrees for the ‘a’ and the ‘D’ have 17,393 and 20,813 cellsrespectively, while their corresponding bi-quadratic ADFs have 457 and399 cells. Bi-quadratic ADFs typically require 5–20 times fewer cellsthan the prior art bi-linear representation of Frisken et al.,“Adaptively Sampled Distance Fields: a General Representation of Shapefor Computer Graphics,” Proceedings ACM SIGGRAPH 2000, pp. 249–254,2000.

Bi-Quadratic Reconstruction Method

Frisken et al. use a quadtree for the ADF spatial hierarchy, andreconstruct distances and gradients inside each cell from the distancessampled at the four corners of each cell via bi-linear interpolation.They suggest that “higher order reconstruction methods . . . might beemployed to further increase compression, but the numbers alreadysuggest a point of diminishing return for the extra effort”.

However, bi-linear ADFs are inadequate for representing, rendering,editing, and animating character glyphs according to the invention. Inparticular, they require too much memory, are too inefficient toprocess, and the quality of the reconstructed field in non-edge cells isinsufficient for operations such as dynamic simulation.

A “bounded-surface” method can force further subdivision in non-edgecells by requiring that non-edge cells within a bounded distance fromthe surface, i.e., an edge, pass an error predicate test, see Perry etal., “Kizamu: A System for Sculpting Digital Characters,” ProceedingsACM SIGGRAPH 2001, pp. 47–56, 2001. Although the bounded-surface methodreduces the error in the distance field within this bounded region, wehave found that for bi-linear ADFs that method results in anunacceptable increase in the number of cells.

To address those limitations, we replace the bi-linear reconstructionmethod with a bi-quadratic reconstruction method. Bi-quadratic ADFs oftypical glyphs tend to require 5–20 times fewer cells than bi-linearADFs. Higher reduction in the required number of cells occurs when werequire an accurate distance field in non-edge cells for operations suchas dynamic simulation and animated type.

This significant memory reduction allows the glyphs required for atypical animation to fit in an on-chip cache of modem CPUs. This has adramatic effect on processing times because system memory access isessentially eliminated, easily compensating for the additionalcomputation required by the higher order reconstruction method.

FIG. 3 illustrates a bi-quadratic ADF cell 300 according to ourpreferred embodiment. Each cell in the bi-quadratic ADF contains ninedistance values 301. A distance and a gradient at a point (x, y) 302 arereconstructed from these nine distance values according to Equations 1–3below.

There are a variety of bi-quadratic reconstruction methods available. Weuse a bivariate interpolating polynomial which guarantees C⁰ continuityalong shared edges of neighboring cells of identical size. As with thebi-linear method, continuity of the distance field between neighboringcells of different size is maintained to a specified tolerance using anerror predicate. The error predicate controls cell subdivision duringADF generation, see Perry et al., above.

The distance and gradient at the point (x, y) 302, where x and y areexpressed in cell coordinates, i.e., (x, y)ε[0,1]×[0,1], are determinedas follows:Let xv ₁ =x−0.5 and xv ₂ =x−1Let yv ₁ =y−0.5 and yv ₂ =y−1Let bx ₁=2xv ₁ ·xv ₂ , bx ₂=−4x·xv ₂, and bx ₃=2x·xv ₁Let by ₁=2yv ₁ ·yv ₂ , by ₂=−4y·yv ₂, and by ₃=2y·yv ₁dist=by ₁·(bx ₁ ·d ₁ +bx ₂ ·d ₂ +bx ₃ ·d ₃)+by ₂·(bx ₁ ·d ₄ +bx ₂ ·d ₅+bx ₃ ·d ₆)+by ₃·(bx ₁ ·d ₇ +bx ₂ ·d ₈ +bx ₃ ·d ₉)  (1)grad_(x) =−[by ₁·(4x·(d₁−2d ₂ +d ₃)−3d ₁ −d ₃+4d ₂)+by ₂·(4x·(d ₄−2d ₅+d ₆)−3d ₄ −d ₆+4d ₅)+by ₃·(4x·(d ₇−2d ₈ +d ₉)−3d ₇ −d ₉+4d ₈)]  (2)grad_(y)=−[(4y−3)·(bx ₁ ·d ₁ +bx ₂ ·d ₂ +bx ₃ ·d ₃)−(8y−4)·(bx ₁ ·d ₄+bx ₂ ·d ₅ +bx ₃ ·d ₆)+(4y−1)·(bx ₁ ·d ₇ +bx ₂ ·d ₈ +bx ₃ ·d ₉)].  (3)

Reconstructing a distance using floating point arithmetic can require˜35 floating-point operations (flops), and reconstructing a gradientusing floating point arithmetic can require ˜70 flops. Because ourreconstruction methods do not contain branches and the glyphs can resideentirely in an on-chip cache, we can further optimize thesereconstruction methods by taking advantage of special CPU instructionsand the deep instruction pipelines of modem CPUs. Further, we canreconstruct a distance and a gradient using fixed-point arithmetic.

Compression for Transmission and Storage

Linear Quadtrees

The spatial hierarchy of the ADF quadtree is required for someprocessing, e.g., collision detection, but is unnecessary for others,e.g., cell-based rendering as described below.

To provide compression for transmission and storage of ADF glyphs, weuse a linear quadtree structure, which stores our bi-quadratic ADF as alist of leaf cells. The tree structure can be regenerated from the leafcells as needed.

Each leaf cell in the linear ADF quadtree includes the cell's x and ypositions in two bytes each, the cell level in one byte, the distancevalue at the cell center in two bytes, and the eight distance offsetsfrom the center distance value in one byte each, for a total of 15 bytesper cell.

Each distance offset is determined by subtracting its correspondingsample distance value from the center distance value, scaling by thecell size to reduce quantization error, and truncating to eight bits.The two bytes per cell position and the one byte for cell level canrepresent ADFs up to 2¹⁶×2¹⁶ in resolution. This is more than adequatefor representing glyphs to be rendered at display screen resolutions.

Glyphs can be accurately represented by 16-bit distance values. Encodingeight of the distance values as 8-bit distance offsets providessubstantial savings over storing each of these values in two bytes.Although, in theory, this may lead to some error in the distance fieldof large cells, we have not observed any visual degradation.

A high-resolution glyph typically requires 500–1000 leaf cells. Losslessentropy encoding can attain a further 35–50% compression. Consequently,an entire typeface of high-resolution ADFs can be represented in 300–500Kbytes. If only body type is required or the target resolution is verycoarse, as for cell phones, then lower resolution ADFs can be used thatrequire ¼ to ½ as many cells.

These sizes are significantly smaller than grayscale bitmap fonts, whichrequire ˜0.5 Mbytes per typeface for each point size, and are comparablein size to well-hinted outline-based fonts. Sizes for TrueType fontsrange from 10's of Kbytes to 10's of Mbytes depending on the number ofglyphs and the amount and method of hinting. Arial and Times New Roman,two well-hinted fonts from the Monotype Corporation, require 266 Kbytesand 316 Kbytes respectively.

Run-Time Generation from Outlines

According to our invention, and as described in detail below, ADFs canbe generated quickly from existing outline or boundary descriptors,e.g., Bezier curves, using the tiled generator described by Perry et al.The minimum distance to a glyph's outline or boundary is computedefficiently using Bezier clipping, see Sederberg et al., “GeometricHermite Approximation of Surface Patch Intersection Curves,” CAGD, 8(2),pp. 97–114, 1991.

Generation requires 0.04–0.08 seconds per glyph on a 2 GHz Pentium IVprocessor. An entire typeface can be generated in about four seconds.Because conventional hints are not needed, the boundary descriptorsrequired to generate the ADFs are substantially smaller than theircorresponding hinted counterparts.

Therefore, rather than storing ADFs, we can store these minimal outlinesand generate ADF glyphs dynamically from these outlines on demand. Thereduced size of these minimal outlines is important for devices withlimited memory and for applications that transmit glyphs across abandwidth-limited network.

FIG. 10 shows a method 1000 for converting a two-dimensional object,such as a glyph, to a two-dimensional distance field. The object 1001 isrepresented as a set of boundary descriptors, e.g., splines, and a fillrule, e.g., an even-odd rule or a non-zero winding rule.

The set of boundary descriptors are first preprocessed 1010. Thepreprocessing subdivides the boundary descriptors to reduce theirspatial extent. The boundary descriptors can also be coalesced to reducethe cardinality of the set of boundary descriptors. The preprocessingallows us to reduce the number of boundary descriptors that need to bequeried for each location when determining the unsigned distance, asdescribed below.

A spatial hierarchy 1021, e.g., a quadtree, is constructed 1020 from thepreprocessed set of boundary descriptors 1011. A cache of intersections1031 is initialized 1030. The cache of intersections 1031 storeslocations where the boundary descriptors intersect a set of lines, e.g.,horizontal, vertical, diagonal, etc., of the distance field, and thedirection of the intersection. This eliminates redundant computationswhen determining the sign of the unsigned distances. The intersectionscan be sorted by intervals.

The spatial hierarchy 1021 is then queried 1040 at a set of locations todetermine a set of distances at those locations. The set of distances isused to construct a two-dimensional distance field 1041. The queryinginvokes a distance function, e.g., Bezier clipping, at each location todetermine an unsigned distance. The cache of intersections, thelocation, and the fill rule are used to determine a sign for thedistance.

Compression Via Component-Based Fonts

Significant compression for Chinese, Japanese, and Korean fonts, whichcan consist of 10,000 or more glyphs, can be achieved by using acomponent-based representation as in Font Fusion. That representationdecomposes glyphs into common strokes and radicals, i.e., complex shapescommon to multiple glyphs, stores the strokes and radicals in a fontlibrary, and then recombines them in the font rendering engine.

Because distance fields are an implicit representation, ADFs can beeasily combined using blending or CSG operations, and thus are wellsuited for compression via that component-based approach.

Representing Corners in a Two Dimensional Distance Field

Detail-directed sampling with a bilinear or bi-quadratic reconstructionmethod allows ADFs to represent relatively smooth sections of a boundaryof a two-dimensional object with a small number of distance values.However, near corners, the distance field has a high variance that isnot well approximated by these reconstruction methods. In order torepresent the distance field near corners accurately, such ADFs requirecells containing corners to be highly subdivided, significantlyincreasing memory requirements. In addition, a maximum subdivision levelof the ADF, imposed during ADF generation as described in Perry et al.,limits the accuracy with which corners can be represented using bilinearand bi-quadratic ADF cells.

To address this problem, our invention provides a method 1300 forgenerating a two-dimensional distance field within a cell associatedwith a corner of a two-dimensional object, such as a glyph.

As shown in FIG. 13, the method 1300 determines 1310 an ordered set ofboundary descriptors 1311 from the two-dimensional object and identifies1320 a corner point 1321 associated with, e.g., near or within, a cellfrom the ordered set of boundary descriptors 1311. The cell is thenpartitioned 1330 into two regions, a first region nearest the corner anda second region nearest the boundary of the object. The method 1300 alsospecifies 1340 a reconstruction method and a set of sampled distancevalues 1371 for reconstructing distances within the cell and stores 1380the corner point 1321, lines delimiting the regions, the reconstructionmethod, and the set of sampled distance values 1371 in a memory.

The reconstruction method determines a distance at a point within thecell according to which region the point lies in. A distance for a querypoint in the first region is determined as the distance from the querypoint to the corner point.

For determining distances in the second region, we partition 1350 theordered set of boundary descriptors 1311 into two subsets, onecomprising boundary descriptors before the corner point 1321 and onecomprising boundary descriptors after the corner point 1321. Each subsetof boundary descriptors is then extended 1360 to form an extended curvethat partitions the cell into an interior and exterior section. For eachsection, the distance field within the cell can be reconstructed fromthe set of sample distance values 1371 that are determined 1370 from thecorresponding extended curve. A bi-quadratic reconstruction method wouldrequire that nine distance values be stored for each of the two extendedcurves.

Note that the intersection of the two interior sections forms the cornerof the object. Hence, distances within the second region can bedetermined by reconstructing a distance to the first interior sectionand a distance to the second interior section and then selecting theminimum of the two determined distances.

The two regions can be specified from two directed lines passing throughthe corner point, each line perpendicular to one of the two subsets ofboundary descriptors. Each line can be specified by the corner point andthe outward facing normal of the corresponding subset of boundarydescriptors at the corner point. When a line is thus defined, we candetermine which side of the line a query point lies on by determining across product of a vector from the query point to the corner point andthe outward facing normal. Points lying on the exterior side of bothlines lie in the first region while points lying on the interior side ofeither line lie in the second region.

FIGS. 21A–21D illustrate a representation of a corner cell. In FIG. 21A,a cell 2102 contains a portion of an object 2104, where an inside of theobject 2104 is shaded and an outside is left white. A boundary of theobject 2104 within the cell 2102 includes a first set of boundarydescriptors 2114, a corner point 2116, and a second set of boundarydescriptors 2118.

A distance field in the cell 2102 of the portion of the object 2104 canbe represented by combining a distance field of an extended curve 2115,illustrated in FIG. 21B, a distance field of an extended curve 2119,illustrated in FIG. 21C, and a distance field of the corner point 2116,illustrated in FIG. 21D. The extended curve 2115 is defined by extendingthe first set of boundary descriptors 2114. Similarly, the extendedcurve 2119 is defined by extending the second set of boundarydescriptors 2118.

In a preferred embodiment, the distance fields of the extended curves2115 and 2119 are each represented using a set of sampled distances anda reconstruction method such as a bilinear or bi-quadraticreconstruction method, while the distance field of the corner point 2116is represented by a procedure for determining a signed distance from asample point to the corner point 2116.

A sign of the distance field of the corner point 2116 can be determinedfrom an angle of the corner represented by the corner point 2116. If theangle of the corner measured on the outside of the portion of the object2104 is acute, then the sign of the distance field of the corner point2116 is positive. If the angle of the corner measured on the outside ofthe portion of the object 2104 is obtuse, then the sign of the distancefield of the corner point 2116 is negative. For example, the cornerrepresented by the corner point 2116 is obtuse and the sign of thedistance field of the corner is negative.

The distance fields of the extended curves 2115 and 2119 and the cornerpoint 2116 each have a valid area and an invalid area. The valid areasand the invalid areas are separated by a first line defined by a normalvector 2120 to the extended curve 2115 and a second line defined by anormal vector 2122 to the extended curve 2119, both lines passingthrough the corner point 2116.

FIGS. 21B, 21C, and 21D show shaded invalid areas 2124, 2126, and 2128and unshaded valid areas 2130, 2132, and 2134 for the extended curves2115 and 2119 and the corner point 2116, respectively. The first andsecond regions, defined above for the method 1300, can be determinedfrom the valid areas. The first region, i.e., the region of the cellnearest the corner point 2116, is the same as the valid area 2134 of thecorner point 2116. The second region, i.e., the region of the cellnearest the boundary of the object 2104, is a union of the valid area2130 of the extended curve 2115 and the valid area 2132 of the extendedcurve 2119.

In one embodiment of the invention, to determine a distance at a samplepoint in the cell 2102, we reconstruct a first signed distance and afirst corresponding validity flag from the distance field of theextended curve 2115, a second signed distance and a second correspondingvalidity flag from the distance field of the extended curve 2119, and athird signed distance and a third corresponding validity flag from thedistance field of the corner point 2116. The first, second, and thirdvalidity flags are determined according to whether the sample point liesinside or outside the valid areas of the extended curve 2115, theextended curve 2119, and the corner point 2116, respectively. Thedistance from the sample point to the portion of the object 2104 is aminimum of the valid first, second, and third signed distances for thesample point.

Representing Stems and other Thin Structures in a Two DimensionalDistance Field

Using corner cells enables the ADF to represent corners accuratelywithout excessive subdivision of cells. However, in addition to corners,two-dimensional objects such as glyphs can have thin structures such asvertical stems or horizontal bars. Near such structures, the distancefield can be C¹ discontinuous. The distance field is C¹ discontinuous ata point when a gradient at the point is singular, i.e., not continuous.

For example, the distance field is C¹ discontinuous along a curve midwaybetween boundary descriptors on either side of a thin structure. Becausethis discontinuity can require excessive subdivision of the cells of theADF, there is a need for a better cell representation and reconstructionmethod near thin structures.

Our present invention provides a ‘two-segment cell’ representation and atwo-segment cell reconstruction method for cells near thin structures.FIGS. 22A, 22B, and 22C illustrate a two-segment cell according to ourpresent invention.

In FIG. 22A, a cell 2202 contains a portion of an object 2206, where theinside of the object 2206 is shaded and the outside is left white. Theboundary of the portion of the object 2206 in the cell 2202 includes afirst set of boundary descriptors including a first segment 2214 and asecond set of boundary descriptors including a second segment 2216.

A distance field of the portion of the object 2206 within the cell 2202can be represented by combining a distance field of the first segment2214, illustrated in FIG. 22B, and a distance field of the secondsegment 2216, illustrated in FIG. 22C. In a preferred embodiment, thedistance fields of the first segment 2214 and the second segment 2216are each represented using a set of sampled distances and areconstruction method, such as a bi-linear or a bi-quadraticreconstruction method.

To determine a distance from a sample point to the portion of the object2206 in the cell 2202, we reconstruct, at the sample point, a firstsigned distance from the distance field of the first segment 2214 and asecond signed distance from the distance field of the second segment2216.

In FIG. 22B, a positive area 2220 of the signed distance field for thefirst segment 2214 is shaded, and a negative area 2222 is left white. InFIG. 22C, a positive area 2230 of the signed distance field for thesecond segment 2216 is shaded, and a negative area 2232 is left white.The portion of the object 2206 in the cell 2202 is an intersection ofthe shaded positive area 2220 of FIG. 22B and the shaded positive area2230 of FIG. 22C. In the preferred embodiment, a distance from thesample point to the portion of the object 2206 in the cell 2202 is aminimum of the first signed distance and the second signed distance.

FIG. 23 illustrates a method 2300 for generating a two-dimensionaldistance field within a two-segment cell 2302 associated with atwo-dimensional object 2301. A set of boundary descriptors 2311 isdetermined 2310 for the object 2301. The boundary descriptors 2311 canhave various representations, including line segments and spline curves,e.g., Bezier curves.

The boundary descriptors 2311 are partitioned 2320 into a set ofsegments 2321, where segments in the set of segments 2321 are delimitedby a set of features that can be determined in a preprocessing step orduring the partitioning 2320. Examples of features include corners ofthe object 2301, points where the boundary descriptors 2311 have asubstantial degree of curvature, an endpoint of a particular boundarydescriptor, or a point on a particular boundary descriptor where anaccumulated curvature along a particular segment exceeds a predeterminedthreshold. Placing a feature at a point of substantial accumulatedcurvature enables, for example, delimiting a segment if the segmentbegins to curve back on itself, e.g., if a magnitude of the accumulatedcurvature of the segment exceeds ninety degrees.

We identify 2330 a first segment 2331 and a second segment 2332 in theset of segments 2321 for the cell 2302. In a preferred embodiment, theidentifying 2330 locates a nearest segment from the set of segments 2321for each test point in a set of test points within the cell 2302 bydetermining a distance from each test point to each segment in the setof segments 2321. If every test point in the cell 2302 is nearest to oneof two particular segments in the set of segments 2321, then we identify2330 the two particular segments as the first segment 2331 and thesecond segment 2332 for the two-segment cell.

We specify 2340 a first set of distance values 2341 to represent adistance field of the first segment 2331, and a second set of distancevalues 2342 to represent a distance field of the second segment 2332.For example, a set of nine distance values can be specified 2340together with a bi-quadratic reconstruction method to represent adistance field corresponding to one of the segments.

The method 2300 defines 2350 a reconstruction method 2351 for combiningthe first set of distance values 2341 and the second set of distancevalues 2342 to reconstruct the distance field within the cell 2302. In apreferred embodiment, the reconstruction method 2351 reconstructs thedistance field at a sample point in the cell 2302 by determining a firstdistance from the sample point to the first segment 2331 using the firstset of distance values 2341, determining a second distance from thesample point to the second segment 2332 using the second set of distancevalues 2342, and combining the first distance and the second distance bytaking a minimum of the first distance and the second distance.

The set of distance values 2341, the set of distance values 2342, andthe reconstruction method 2351 are stored 2360 in a memory 2370 toenable reconstruction of the two-dimensional distance field of thetwo-dimensional object 2301 within the cell 2302.

Determining an Optimal Configuration of Cells for Distance Fields withSpecialized Cells

Using specialized cells such as corner cells and two-segment cells canmitigate excessive subdivision of cells of an ADF representing anobject, such as a glyph, with corners and thin structures. However,determining an optimal configuration of cells for a distance field thatuses such specialized cells can be significantly more complicated thandetermining an optimal configuration of cells without specialized cells.A configuration of cells for a distance field includes, for example,locations, sizes, orientations, reconstruction methods, types, andgeometries for the cells.

There are many possible cell configurations for partitioning a regioncontaining a distance field representing an object. The prior art ofFrisken et al. teaches a top-down and a bottom-up subdivision methodthat partitions the region into rectangular cells to generate aquadtree-based or octree-based ADF, thereby providing a non-optimalconfiguration without specialized cells. Unlike the prior art, thepresent invention provides a method for generating a cell-based distancefield representation with an optimal configuration of cells. In thepreferred embodiment, the optimal configuration can include specializedcells such as corner cells and two-segment cells.

FIG. 24A illustrates a region 2460 containing a portion of atwo-dimensional object 2401, where an inside of the object is shaded andan outside is left white. A boundary of the portion of the object 2401within the region 2460 includes a first segment 2406 associated with afirst set of boundary descriptors, a second segment 2408 associated witha second set of boundary descriptors, and a third segment 2410associated with a third set of boundary descriptors. The first segment2406 and the second segment 2408 meet at a corner 2412 of the portion ofthe object 2401, while the second segment 2408 and the third segment2410 meet at a corner 2414 of the portion of the object 2401.

There are many ways to partition the region 2460 to determine aconfiguration of cells. FIGS. 24B–24D show various configurations ofcells that partition the region 2460 when the configurations can includetwo-segment cells and corner cells. A particular definition of ‘optimal’for an optimal configuration depends on many factors, some of which areillustrated in FIGS. 24B–24D, and others of which are discussed below.

FIG. 24B shows a Voronoi diagram for the boundary of the object 2401within the region 2460. Each differently shaded cell shows a portion ofthe region 2460 nearest to a particular segment or corner. Points in acell 2420 are nearest to the segment 2406. Points in a cell 2422 arenearest to the segment 2408. Points in a cell 2424 are nearest to thesegment 2410. Points in a cell 2426 are nearest to the corner 2412.Finally, points in a cell 2428 are nearest to the corner 2414.

The Voronoi diagram of FIG. 24B is an example of an optimalconfiguration of cells for the region 2460 when the configuration usesonly ‘one-segment cells’, a one-segment cell defined to be a cell forwhich the distance field within the cell can be determined from a singlesegment. Distances in a one-segment cell can be reconstructed from a setof sampled distance values using, for example, a bi-quadraticreconstruction method when the segment nearest to the cell has asubstantially low curvature. Various alternative reconstruction methodsare also possible, including an analytic determination of the distancefrom points in the cell to the segment nearest to the cell.

The Voronoi diagram of FIG. 24B is an optimal configuration of cells inthe sense that it provides a minimal number of cells from which thedistance field of the portion of the object 2401 can be reconstructedaccurately everywhere in the region 2460 using one-segment cells. Adisadvantage of using the Voronoi diagram to partition the region 2460is that determining an exact configuration of the Voronoi diagram isdifficult. A second disadvantage of using the Voronoi diagram is thatcells can have very complex boundaries, thereby resulting insubstantially long computation times for rasterizing and locating cellsduring rendering.

FIG. 24C provides an alternative optimal configuration of cellspartitioning the region 2460 which uses corner cells, as defined above.The region 2460 is partitioned into a first corner cell 2430 and asecond corner cell 2432. Distances within the corner cell 2430 can bereconstructed using the first segment 2406, the corner 2412, and thesecond segment 2408. Distances within the corner cell 2432 can bereconstructed using the second segment 2408, the corner 2414, and thethird segment 2410. Distances within the corner cell 2430 or the cornercell 2432 can be reconstructed to substantially high accuracy fromsampled distance values using a corner cell reconstruction method suchas the one described above.

An advantage of the configuration of cells illustrated in FIG. 24C overthe configurations of FIGS. 24B and 24D is that the configuration inFIG. 24C requires fewer cells. A disadvantage is that corner cellreconstruction methods are usually more complex and inefficient thanone-segment and two-segment reconstruction methods and the configurationof cells of FIG. 24C requires that a corner cell reconstruction methodbe used for all points in the region 2460. A second disadvantage withthe configuration of FIG. 24C is that, like the Voronoi diagram of FIG.24B, cell boundaries may be difficult to determine. A third disadvantageis that cell boundaries may be very complex, thereby resulting insubstantially long computation times for rasterizing and locating cellsduring rendering.

FIG. 24D illustrates a third alternative optimal partitioning of theregion 2460. The region 2460 is partitioned into a quadtree, where eachleaf cell in the quadtree is shaded according to its cell type. A cell2440 is a one-segment cell, with points within the cell nearest to thesegment 2410. A cell 2442 is a two-segment cell, with points within thecell nearest to either the segment 2406 or the segment 2410. Distanceswithin the cell can be reconstructed using a two-segment reconstructionmethod. A cell 2444 is a corner cell, where points within the cell arenearest to either the corner 2412, the segment 2406, or the segment2408. A cell 2446 is also a corner cell, where points within the cellare nearest to either the corner 2414, the segment 2408, or the segment2410. Distances within the cell 2444 and the cell 2446 can bereconstructed using a corner cell reconstruction method.

Cells 2448, 2450, and 2452 are exterior cells, i.e., cells outside ofthe portion of the object 2401 that lie beyond a minimum distance fromthe boundary of the object 2401. If an accurate representation of thedistance field is not needed beyond the minimum distance, then distancesat points in cells 2448, 2450, and 2452 can be approximated by simplerreconstruction methods. For example, the distances at the points can bereconstructed from nine sampled distance values using a bi-quadraticreconstruction method, thereby decreasing memory and computation time.

An advantage of the partitioning illustrated in FIG. 24D is that thecells have simple boundaries and hence are quickly and easily rasterizedand located during rendering. A second advantage is that the quadtreeprovides a spatial data structure that enables fast queries of thedistance field. An advantage over the configuration of FIG. 24C is thatsimple reconstruction methods, e.g., one-segment or bi-quadraticreconstruction methods, are used for some points in the region and morecomplex methods, e.g., two-segment and corner reconstruction methods,are only used when necessary, thereby decreasing computation time. Adisadvantage is that there are more cells in the configuration of FIG.24D than in the configurations of FIGS. 24B and 24C.

As illustrated by the examples shown in FIGS. 24B, 24C, and 24D, whenspecialized cell types are used, there are many optimal configurationsof cells for partitioning a distance field representing an object. Whengenerating a configuration, defining ‘optimal’ depends on many factors,including how the configuration is rendered, edited, and processed.

By optimal configuration, we mean a configuration that balances a set ofdesired characteristics of a cell-based distance field representation.An optimization of the configuration can be guided by minimizing a sizeof the distance field, minimizing a time required to render the distancefield, minimizing a time to generate the distance field, maximizing aquality metric of a rendering of the distance field, minimizing a cellcount, and maximizing an accuracy of the distance field, to name but afew.

FIG. 25 illustrates a method 2500 for generating a cell-based distancefield for a region 2501 of a shape descriptor 2502 representing anobject. A set of cell types 2511 is defined 2510, where the cell typescan include bi-linear and bi-quadratic cell types as well as variousspecialized cell types including corner cell types and two-segment celltypes to name but a few.

The method 2500 generates 2520 a configuration 2521 of a set of cellsfor the region 2501, where each cell in the set of cells has aparticular cell type, as defined by the set of cell types 2511, and areconstruction method 2512 for reconstructing the distance field withinthe cell. The configuration 2521 of the set of cells is modified 2530using the shape descriptor 2502, the region 2501, and the set of celltypes 2511 until an optimal configuration 2531 for the set of cells ofthe region 2501 is reached. The optimal configuration 2531 of the set ofcells is stored 2540 in a memory 2541 to generate the cell-baseddistance field.

Unlike the prior art top-down and bottom-up generation methods describedby Frisken et al., the configuration according to the present inventioncan provide either a complete tessellation or an incomplete tessellationof the region 2501. For example, according to the present invention,both the configuration 2521 and the optimal configuration 2531 can covera subset of the region, leaving areas of the region where the distancefield is not represented, or a superset of the region, providing arepresentation of the distance field outside of the region. Unlike theprior art methods, cells in the present invention can overlap eachother, providing additional opportunities to generate an optimalconfiguration.

The prior art methods are not guided by optimization criteria andtherefore do not produce optimal configurations in any sense. The priorart applies strictly deterministic methods, resulting in configurationsthat are often restricted and sub-optimal. The prior art also does notconsider specialized cells during generation.

To achieve an optimal configuration according to the present invention,both the generating 2520 and the modifying 2530 of the configuration2521 of the set of cells can be done manually by a user, automaticallyby a computer, or semi-automatically, i.e., by computer with input fromthe user. The modifying 2530 can change the configuration 2521 of theset of cells by adding or deleting cells from the configuration 2521 ofthe set of cells or by changing attributes of a particular cell such asthe geometry, the location, the orientation, and the type of theparticular cell. Both the generating 2520 and the modifying 2530 can beperformed using deterministic methods or non-deterministic methodsincluding probabilistic methods and randomized methods.

In one embodiment, the generating 2520 places a single cell at anarbitrary or predetermined location in the region 2501 and the modifying2530 adjusts the cell to an optimal shape and size. The modifying 2530then adds new cells in uncovered areas of the region 2501, adjustingeach of these to optimal shapes and sizes, and repeats this processuntil an optimal configuration 2531 is achieved. In another embodiment,the generating 2520 places an initial set of corner cells near cornerpoints of the shape descriptor 2502 and the modifying 2530 tessellatesthe remaining uncovered area of the region 2501 to determine anotheroptimal configuration 2531. Both of these embodiments provide an optimalconfiguration 2531 that is not possible with the prior art methods ofFrisken et al.

In another embodiment, the generating 2520 can include preprocessing theshape descriptor 2502 to produce a set of preprocessed shape descriptorsand a corresponding set of preprocessed distance procedures that can beused to accelerate both the generating 2520 and the modifying 2530.

For example, the preprocessing can determine boundary descriptors fromthe shape descriptor, partition the boundary descriptors into a set ofsegments delimited by features of the boundary descriptors. The featurescan include corner points, points along the boundary descriptors withsubstantial curvature, endpoints of the boundary descriptors, and pointsof substantial accumulated curvature as described above. The featurescan be changed during the modifying 2530 by adding, deleting, andaltering a particular feature. When the features are changed during themodifying 2530, the set of preprocessed shape descriptors and the set ofpreprocessed distance procedures can be adapted accordingly.

Font Rendering

In today's font rendering engines, fonts are predominantly representedas outlines, which are scaled as needed to match the desired outputssize. While most high-resolution printers use bi-level rendering, moderndisplay devices more commonly use grayscale rendering or a combinationof grayscale and bi-level rendering at small point sizes.

A common approach for rasterizing grayscale glyphs involves scaling andhinting their outlines. The scaled and hinted outlines are scanconverted to a high-resolution image, typically four or sixteen timeslarger than the desired resolution. Then, the high-resolution image isdown-sampled by applying a filtering method, e.g., a box filter, toproduce the final grayscale image.

For body type, individual glyphs can be rasterized once and stored in acache as a grayscale bitmap for reuse in a preprocessing step. The needfor sub-pixel placement of a glyph may require several versions of eachglyph to be rasterized. Use of a cache for body type permits higherquality rendering with short delays, e.g., ½ second, during tasks suchas paging an Adobe Acrobat PDF document.

However, type rendered on arbitrary paths and animated type precludesthe use of a cache and therefore must be generated on demand. Real-timerendering requirements can force the use of a poor filter, e.g., boxfiltering with four samples per pixel, and can preclude the use ofhinting. This can cause spatial and temporal aliasing as well asbaseline jitter and inconsistent stroke weights. The aliasing can bereduced using hinted device fonts residing in system memory. However,maintaining real-time frame rates places severe constraints on howhinted device fonts can be used, e.g., hinted device fonts cannot bescaled or rotated dynamically.

Recent work at Microsoft on ClearType has led to special treatment forLCD color displays that contain a repeating pattern of addressablecolored sub-pixels, i.e., components. Platt, in “Optimal Filtering forPatterned Displays,” IEEE Signal Processing Letters, 7(7), pp. 179–180,2000, describes a set of perceptually optimal filters for each colorcomponent. In practice, the optimal filters are implemented as a set ofthree displaced box filters, one for each color.

ClearType uses prior art hinting and coverage based antialiasing methodsto determine the intensity of each component of each pixel and thus hasall of the disadvantages described above. In contrast, our distancefield based method uses the distance field to determine the intensity ofeach component of each pixel, and does so using fewer samples. Our ADFantialiasing method described below can replace the box filters toprovide better emulation of the optimal filters with fewer samples perpixel.

Antialiasing

Understanding appearance artifacts in rendered fonts requires anunderstanding of aliasing. Typically, a pixel is composed of discretecomponents, e.g., a red, green, and blue component in a color printer ordisplay. In a grayscale device, the pixel is a single discretecomponent. Because pixels are discrete, rendering to an output device isinherently a sampling process. The sampling rate is dependent on theresolution of the device. Unless the sampling rate is at least twice thehighest (Nyquist) frequency in the source signal, the sampled signalexhibits aliasing.

Edges, e.g., glyph outlines, have infinite frequency components. Hence,edges cannot be represented exactly by sampled data. Inadequate samplingof edges results in jaggies, which tend to crawl along the sampled edgesin moving images. If the source signal also contains a spatial pattern,e.g., the repeated vertical stems of an ‘m’ or the single vertical stemof an ‘i’, whose frequency components are too high for the samplingrate, then the sampled data can exhibit dropout, moire patterns, andtemporal flicker.

To avoid aliasing, the input signal must be pre-filtered to removefrequency components above those permitted by the sampling rate. Ingeneral, there are two approaches to pre-filtering.

The first is known as analytic filtering. It applies some form ofspatial averaging to a continuous representation of the source signalbefore sampling. Unfortunately, analytic filtering is often notpossible, either because the source data are not provided as acontinuous signal, which is the normal case for image processing, orbecause determining an analytic description of the signal within thefilter footprint is too complex. This is the case for all but simplegeometric shapes in computer graphics and certainly the case forspline-based outlines.

The second approach is known as discrete filtering. In that approach,the source signal is typically sampled at a higher rate than the targetrate to obtain a supersampled image. Then, a discrete filter is appliedto reduce high frequencies in the supersampled image beforedown-sampling the image to the target rate. The discrete approach isreferred to as regular supersampling in computer graphics.

Various discrete filters can be applied depending on the processingbudget, hardware considerations, and personal preferences for contrastversus smoothness in the output image. The box filter typically used torender type simply replaces a rectangular array of supersampled valueswith their arithmetic average and is generally regarded as inferior inthe signal processing community.

In another approach, adaptive supersampling focuses available resourcesfor sampling and filtering on areas of the image with higher localfrequency components. Optimal adaptive sampling can be determined fromthe local variability in the image. However, the usefulness of thistechnique is limited by the need to estimate the local variance of theimage, a process that can be computationally expensive.

Moiré patterns, due to inadequate regular sampling of high frequencypatterns, are particularly objectionable to the human visual system. Ingeneral image processing, stochastic or jittered sampling has been usedto solve this problem. With stochastic sampling, the samples arerandomly displaced slightly from their nominal positions. Stochasticsampling tends to replace moire pattern aliasing with high frequencynoise and has been shown to be particularly effective in reducingtemporal aliasing.

Rendering with Distance-Based Antialiasing

The infinite frequency components introduced by edges of a glyph are amajor contribution to aliasing in prior art font rendering. In contrast,by using 2D distance fields to represent 2D objects and then samplingthe 2D distance fields according to the invention, we avoid such edgesbecause the representation is C⁰ continuous. Instead, a maximumfrequency depends on a spatial pattern of the glyph itself, e.g., therepeated vertical stems of an ‘m’ or the single vertical stem of an ‘i’.

By representing the glyph by its 2D distance field, we are effectivelyapplying an analytic pre-filter to the glyph. Our antialiasing methodsfor rendering distance fields as described below yield an output that isdifferent from the output of a conventional analytic pre-filter.

Antialiasing with Distance Fields

FIG. 4 shows a method 400 for antialiasing, in image-order, an object401, e.g., a glyph, represented 410 as a two-dimensional distance field411. Each pixel 402 can include one or more components 404, typically ared, blue, and green component for a ‘RGB’ type of output device. Thismethod can use one or more samples for each component 404 of each pixel402. The method 400 provides adaptive distance-based super sampling,distance-based automatic hinting, and distance-based grid fitting. Theresulting antialiased pixel intensity can be rendered on CRT andLCD-like displays as part of an image. The method is particularly usefulfor rendering motion blur.

A set 403 of sample points 407 in the two-dimensional distance field 411representing the object 401 is associated 420 with each component 404 ofeach pixel 402. A distance (D) 405 is determined 430 from thetwo-dimensional distance field 411 and the set of sample points 403.Then, the distance 405 is mapped 440 to an antialiased intensity (I) 406of the component 404 of the pixel 402.

In the preferred embodiment, the glyph 401 is represented 410 by abi-quadratic ADF 411, as described above. This makes it efficient toapply distance-based antialiasing during font rendering. Otherrepresentations such as a two-dimensional distance map, atwo-dimensional distance shell, an optimal ADF including specializedcells, and a procedural distance field can also be used.

For each component 404 of each pixel 402 in an image, a cell, e.g., aleaf cell, containing the component 404 is located using a quadtreetraversal method described in U.S. patent application Ser. No.10/209,302, filed on Jul. 31, 2002 and titled “Method for TraversingQuadtrees, Octrees, and N-Dimensional Bi-trees,” incorporated herein byreference in its entirety. Although other traversal methods known in theart can be used with our invention, the aforementioned method iscomparison-free and therefore executes efficiently. The distance at thecomponent 404 is reconstructed from the cell's distance values andmapped 440 to the antialiased intensity (I) 406.

Different mappings can be used, including linear, Gaussian, andsigmoidal functions. Selection of the best mapping function issubjective. In one embodiment, our mapping is a composition of twofunctions. The first function is as described above, the second is acontrast enhancement function. These two functions are composed to map440 the distance field (D) 405 to the antialiased intensity (I) 406 ofthe component 404.

FIG. 5 shows a linear mapping 500 of intensity 501, e.g., [0,1], as afunction of distance 502. The mapping converts a distance to anantialiased image intensity for each component of the pixel. Distancesare positive inside the object and negative outside the object.Different cutoff values 503 and 504 affect the edge contrast and strokeweight. We achieve good results with outside 503 and inside 504 filtercutoff values of (−0.75, 0.75) pixels for display type, and (−0.5,0.625) pixels for body type.

The mapping 440 can be chosen with a user interface that allows adisplay manufacturer to tune the mapping 440 for their displays.Similarly, the user interface can be provided at an application oroperating system level to enable each user the ability to optimize themapping 440 to their personal preferences.

Optimal Distance-Based Adaptive Supersampling

The above described distance-based antialiasing method reduces aliasingdue to glyph edges. However, aliasing artifacts still occur when stemwidths or spacing between glyph components are too small for thedisplay's sampling rate. In such cases, we apply distance-based adaptivesupersampling as described below to further reduce spatial and temporalaliasing.

In the preferred embodiment, we use bi-quadratic ADFs with our noveldistance-based adaptive supersampling to provide significant advantagesover prior art outline-based representations and coverage-based adaptivesupersampling methods. Because ADFs use detail-directed sampling,regions of the distance field with higher local variance are representedby smaller leaf cells. Hence, the structure of the ADF quadtree providesthe map of local variance required to implement optimal distance-basedadaptive sampling, overcoming the difficulty in the prior art adaptivesupersampling antialiasing methods of determining the local variance asdescribed above.

For each component 404 of each pixel 402 in the image, the cellcontaining the component 404 is located, and a set 403 of sample points407 within a filter radius, r, of the component is associated 420 withthe pixel component 404. The number of sample points 407 per component(spc) depends on the relative size of the cell (cellSize) to r. Sampleddistances at the sample points 407 are filtered to determine 430 asingle weighted average distance 405 that is then mapped 440 to anantialiased intensity 406 of the component 404 of the pixel 402.

Various filters and sampling strategies are possible. In the preferredembodiment we use a general form of a Gaussian filter, weighting eachdistance sample by W⁻¹2^(−3(d/r)) ₂ , where d is the distance from thesample point to the component of the pixel and W is the sum of theweights used for that component. Similar results can be obtained withbox filters, cone filters, negative lobe filters, and other forms of theGaussian filter.

FIG. 6A–C shows our sampling strategy. Samples 407 are placed inconcentric circles 610 near the component 601 for efficient computationof the weights and weight sums. We use a filter radius r 602 of 1.3times the inter-pixel spacing and sample with 1 spc when cellSize>r(FIG. 6A), 5 spc when r/2<cellSize≦r (FIG. 6B), and 13 spc whencellSize≦r/2 (FIG. 6C).

Rather than concentric circles, the invention can use numerous otherstrategies to associate sample points 407 with pixel components 404. Ourmethod is not particularly sensitive to the exact sampling strategy.

Another adaptive sampling strategy, described below, places samplepoints at the centers of all the cells contained within the filterradius r. This strategy has equally good results.

Cell-Based Antialiasing

The distance field antialiasing methods described above can beimplemented in software using scanline-based rasterization.Alternatively, distance fields partitioned into cells, e.g., abi-quadratic ADF or an optimal ADF including specialized cells, can beantialiased cell-by-cell, i.e., in object-order. Cell-based renderingeliminates tree traversal for locating cells containing the samplepoints, eliminates redundant setup for computing distances and gradientswithin a single cell, and reduces repeated retrieval, i.e., memoryfetches, of cell data.

In addition, because the cells required for rendering can be representedas a sequential block of fixed sized, self-contained units, i.e.,distances and gradients for points within a cell are determined from thecell's distance values, our cell-based approach is amenable to hardwareimplementations, enabling real-time rendering.

FIG. 7 shows a method 700 for antialiasing an object 701, e.g., a glyph,represented 710 as a two-dimensional distance field 711 in object-order.The method 700 provides adaptive distance-based super sampling,distance-based automatic hinting, and distance-based grid fitting. Theresulting antialiased pixel intensity can be rendered on CRT andLCD-like displays as part of an image. The method is particularly usefulfor rendering motion blur. We can use mipmapping when the cells of thetwo-dimensional distance fields 711 are organized in a spatial hierarchyto reduce the number of distance samples required.

The two-dimensional distance field 711 is partitioned into cells 712. Ina preferred embodiment where we use bi-quadratic, adaptively sampleddistance fields, the size of each cell is dependent on a local varianceof the two-dimensional distance field. Each cell includes a method (M)713 for reconstructing the two-dimensional distance field within thecell. A set of cells 721 containing a region (dashed line) 722 of thedistance field to be rendered is identified 720.

The region 722 is used to locate 730 a set of pixels 731 associated withthe region. A set of components 741 for each pixel in the set of pixels731 is specified 740. Then, antialiased intensities 751 are determined750 for each component of each pixel from distances in the set of cells.Here, the distances are reconstructed from the set of cells. Thedistances are then mapped to the antialiased intensity, as describedabove.

In one embodiment, we can determine the distance by locating a singlesample point within the set of cells near the component of the pixel andreconstructing the distance at the single sample point from the set ofcells. In this embodiment, the two-dimensional distance field 711 can berepresented as an optimal ADF including specialized cells.

In our preferred embodiment where we use bi-quadratic adaptively sampleddistance fields, this approach is augmented with a special treatment ofcells smaller than the filter radius for adaptive distance-basedsupersampling. Because small cells occur where there is high variance inthe distance field, distances in pixels near these cells can bepre-filtered before mapping the distances to intensity.

We initialize a compositing buffer of elements, where each elementcorresponds to a component of each pixel of the set of pixels. Each cellin the set of cells can be processed independently. In the preferredembodiment, each element consists of a weighted distance and anaccumulated weight which are both initialized to zero. When a cell isprocessed, these weighted distances and accumulated weights areincremented in the buffer elements that correspond to pixel componentswhich lie either within the cell or within a filter radius of the cell'scenter.

After processing all the cells, the weighted distances are normalized bythe accumulated weight for each component of each pixel to produce thedistance that is then mapped to the antialiased component intensity. Inthe preferred embodiment, we use the same Gaussian weights and filterradius as described above.

Our cell-based rendering described thus far always processes every leafcell in the set of cells, regardless of the relative sizes of each cellto the filter radius. In theory, this provides optimal adaptivedistance-based supersampling. In practice, the ADF quadtree can be usedas a mipmap to reduce the number of cells.

The ADF quadtree structure allows us to replace small leaf cells withtheir ancestors, effectively truncating the quadtree at somepredetermined cell size. As long as this cell size is less than or equalto ¼ of the inter-pixel spacing, there is no visual degradation in theadaptive distance-based supersampling results. This reduces the numberof cells to render the region.

Rendering Overlapping Objects Represented as Two-Dimensional DistanceFields

The present invention provides methods and apparatuses for renderingoverlapping objects represented as two-dimensional distance fields thatavoid the problems in the prior art. In particular, rather than blendingcolor or intensity values derived from coverage-based antialiasing andrather than combining the overlapping objects into a single compositeobject prior to rendering, the present invention combines distancevalues that are determined on-demand during rendering for a component ofa pixel. A combined distance is then mapped to determine an antialiasedintensity of the component of the pixel.

FIGS. 14A and 14B show a method 1400 for rendering, in image-order, aset of objects 1410. Referring to FIG. 14A, the set of objects 1410 isrepresented 1420 by a set of two-dimensional distance fields 1430, therebeing one distance field for each object, e.g., a distance field 1431corresponds to an object 1411, and a distance field 1433 corresponds toan object 1413.

As shown in FIG. 14B, each pixel 1404 can include one or more components1406, typically a red, green, and blue component for RGB rendering. Themethod 1400 determines an antialiased intensity 1402 of a component 1406of a pixel 1404. Sets of sample points 1441–1443 are associated 1440with the pixel component 1406, there being a one-to-one correspondencebetween each set of sample points and each distance field in the set oftwo-dimensional distance fields 1430. For example, the set of samplepoints 1441 corresponds to the distance field 1431 and the set of samplepoints 1443 corresponds to the distance field 1433.

A corresponding distance is then determined 1450 for each distance field1431–1433 using its corresponding set of sample points 1441–1443,producing corresponding distances 1451–1453. For example, thecorresponding distance 1451 is determined 1450 for the distance field1431 using its corresponding set of sample points 1441.

The corresponding distances 1451–1453 are then combined 1460 todetermine a combined distance 1461. The combined distance 1461 is thenmapped 1470 to determine the antialiased intensity 1402 of the component1406 of the pixel 1404.

FIGS. 15A, 15B, and 15C show a method 1500 for rendering, inobject-order, a set of objects 1510. Referring to FIG. 15A each object1511–1513 in the set of objects 1510 is represented 1501 by acorresponding two-dimensional distance field 1521–1523. Thecorresponding two-dimensional distance fields 1521–1523 constitute a setof two-dimensional distance fields 1520. For example, the distance field1521 corresponds to the object 1511 and the distance field 1523corresponds to the object 1513.

Referring to FIG. 15B, each distance field 1521–1523 in the set oftwo-dimensional distance fields 1520 is partitioned 1525 into cells,where each cell is associated 1530 with a method for reconstructing 1531the two-dimensional distance field within the cell.

As shown in FIG. 15C, to render a region 1545 of the set of objects1510, a set of pixels 1551 is located 1550 and a set of components 1560for each pixel in the set of pixels 1551 is specified 1555. Note thateach pixel in the set of pixels 1551 can include one or more components,typically a red, green, and blue component for RGB rendering. The method1500 determines an antialiased intensity 1566 for each component 1561 ofeach pixel in the set of pixels 1551.

For each two-dimensional distance field 1521–1523 in the set oftwo-dimensional distance fields 1520, a corresponding set of cells1541–1543 associated with the region 1545 is identified 1540, e.g., theset of cells 1541 is identified 1540 for the distance field 1521 and theset of cells 1543 is identified 1540 for the distance field 1523.

For each component 1561 of each pixel in the set of pixels 1551, anantialiased intensity 1566 is determined 1565 by first determining 1570,for the component 1561, a corresponding distance 1571–1573 for eachdistance field 1521–1523 using the corresponding set of cells 1541–1543.For example, the corresponding distance 1571 is determined 1570 for thecomponent 1561 for the distance field 1521 using the set of cells 1541.

The corresponding distances 1571–1573 are then combined 1575 todetermine a combined distance 1576. The combined distance 1576 is thenmapped 1580 to produce the antialiased intensity 1566 of the component1561 of the pixel.

Unlike the prior art, which renders overlapping regions by blending orcombining color or intensity values of the rendered objects or bycombining coverage-based antialiased values, the methods 1400 and 1500combine distance values, thus mitigating color artifacts and blendingartifacts exhibited by the prior art.

Unlike the prior methods of Perry et al., the methods 1400 and 1500 donot generate a combined distance field to represent the composite objectprior to rendering. Instead, according to our present invention, acombined distance is determined on-demand during rendering for acomponent of a pixel by combining distances determined for thecomponent.

There are several methods for combining 1460 the corresponding distances1451–1453 and combining 1575 the corresponding distances 1571–1573. Forexample, using a positive-inside, negative-outside sign convention forthe distance fields, the combining can take a maximum of thecorresponding distances to produce a union of the objects or a minimumof the corresponding distances to produce an intersection of theobjects. Other combining methods include taking a difference, performingan arithmetic average, or performing an implicit blend of thecorresponding distances, to name but a few.

An implicit blend can be used to round corners between the objects whilean arithmetic average can be used to provide additional antialiasing byfurther reducing high frequency content in the rendered region. Moregenerally, the combining can be any arithmetic or conditional operation.Furthermore, the combining can use a procedure or a table to determinethe combined distance.

Rendering Cell-Based Distance Fields Using Texture Mapping

The present invention can render a distance field representing anobject, such as a two-dimensional glyph, using texture mapping, wherethe texture mapping constitutes one stage in a multi-stage renderingpipeline. We first provide an overview of each stage of the renderingpipeline, and then describe specific details of various stages alongwith several embodiments of the invention.

FIGS. 16A and 16B show a method 1600 for rendering a distance field 1602representing an object 1603 according to the invention.

As shown in FIG. 16A, the distance field 1602 is partitioned into a setof cells 1606, where each cell 1604 includes a set of distance samples1605 and a method for reconstructing the distance field 1602 within thecell 1604 using the distance samples 1605.

A region 1601 of the distance field 1602 representing the object 1603 isdefined. To render the region 1601, we proceed to a first stage in therendering pipeline, and then to subsequent stages in order.

The first stage selects 1610 a set of source cells 1611 from the set ofcells 1606 of the distance field 1602. The selection 1610 enables arendering of the region 1601. For example, the set of source cells 1611covering the region 1601 can be selected 1610.

In FIG. 16B, a second stage represents 1620 each source cell 1612 in theset of source cells 1611 as a geometric element 1621 defined in a worldcoordinate system. Each geometric element 1621 is associated 1622 with atexture map 1623, where the texture map 1623 includes distance samples1605 of the corresponding source cell 1612.

The geometric element 1621 can be described as a quadrilateral, atriangle, a polygon, a set of control vertices constituting a shape withcurved edges, to name but a few. The description of the geometricelement 1621 is typically chosen to match the geometry of thecorresponding source cell 1612, although the present invention is notlimited to this approach.

A third stage transforms 1630 each geometric element 1621 from the worldcoordinate system to a geometric element 1631 in a pixel coordinatesystem. There are many ways to perform the transformation 1630 asdescribed below.

A fourth stage texture maps 1640 each geometric element 1631 todetermine a distance 1641 for each component 1642 of each pixel 1643associated with the geometric element 1631. The texture mapping 1640involves rasterizing the geometric element 1631 to produce pixels 1643associated with the geometric element 1631 and then determining “colors”of the pixels 1643. In actuality, in the present invention, the colorsof the pixels 1643 represent distance values 1641 of the components 1642of the pixels 1643. The texture mapping 1640 uses the distance samples1605 stored in the texture map 1623 to perform a reconstruction of thedistance field 1602 within the geometric element 1631 for each component1642 of each pixel 1643 associated with the geometric element 1631.

In a fifth and final stage of the rendering pipeline, we map 1650 thedistance 1641 of each component 1642 of each pixel 1643 to anantialiased intensity 1651 of the component 1642 of the pixel 1643.

The stages of the multi-stage rendering pipeline can be implemented on acentral processing unit, an application specific integrated circuit,fixed-function graphics hardware, programmable graphics hardware, andvarious combinations, to name but a few.

Programmable graphics hardware, see Real-Time Rendering, Akenine-Mollerand Haines, A K Peters, 2002, ISBN 1-56881-182-9, allows thetransforming 1630, the texture mapping 1640, and the mapping 1650 stagesof our multi-stage rendering pipeline to be controlled by vertex andpixel shaders. A vertex shader defines a procedure that operates on ageometric element to produce a transformed geometric element. A pixelshader receives rasterized pixels that can then be manipulated, e.g.,colorized, before their eventual arrival to a frame buffer. Vertex andpixel shaders provide enormous flexibility when rendering an object.

In the present invention, we can exploit both types of shaders toperform various aspects of our rendering pipeline. For example, thetransforming 1630 can be performed by a vertex shader, the texturemapping 1640 can be performed by a pixel shader, and the mapping 1650can be performed by a pixel shader.

The texture mapping 1640 can perform various interpolation methods todetermine the distance 1641 for each component 1642 of each pixel 1643such as bi-linear interpolation, tri-linear interpolation, bi-quadraticinterpolation, high-order, e.g., bi-cubic, interpolation, to name but afew. The texture mapping 1640 either approximates the distance 1641 foreach component 1642 of each pixel 1643, thereby producing a lessfaithful rendering of the object 1603, or determines the distance 1641for each component 1642 of each pixel 1643 exactly. An approximationmethod can be used when the method of reconstruction for a source cell1612 is too complicated to implement or requires too much time toexecute.

When multiple texturing units are available, the texture mapping 1640can determine the distance 1641 of each component 1642 of each pixel1643 concurrently and independently, thereby rendering the object 1603efficiently.

The mapping 1650 can use one-dimensional texture mapping to determinethe antialiased intensity 1651 for each component 1642 of each pixel1643. This one-dimensional texture mapping can be used to approximate afilter function. The mapping 1650 can also use a lookup table or a pixelshader to determine the antialiased intensity 1651 for each component1642 of each pixel 1643.

When rendering multiple distance fields representing multiple objects orwhen rendering composite glyphs represented by a set of distance fields,the distance fields can overlap and must be treated appropriately, seeabove.

FIG. 16C shows an embodiment including additional steps for the method1600 of the present invention to properly handle overlap conditions. Acombining step 1670 is performed after the texture mapping 1650. In thisembodiment, we combine 1670 distances 1661–1663, determined by thetexture mapping 1640, for each component 1642 of each pixel 1643 todetermine a combined distance 1671. We then map 1680 the combineddistance 1671 of each component 1642 of each pixel 1643 to anantialiased intensity 1681 of the component 1642 of the pixel 1643.

Unlike the present invention, prior art font rendering cannoteffectively render high-quality glyphs using hardware. Prior art hintingis too complicated, with many branches in the execution flow andcomplicated data structures, to make hardware an effective solution.

Although the prior art uses texture mapping for many purposes, usingtexture mapping, according to our invention, to render a distance fieldrepresenting an object is unique. Furthermore, the independent andconcurrent determination of distance values for each component of eachpixel, according to our invention, is novel.

Unlike the prior art, our invention enables a rendering of a specializedcell such as a corner cell or a two-segment cell of a distance fieldusing a pixel shader to reconstruct the distance field within the cell.

Rendering Using a Progressive Cache—System Structure

FIG. 17 shows a system 1700 for efficiently rendering a graphics objectrepresented as a two-dimensional distance field. The system 1700includes a rendering pipeline 1710, a cache manager 1720, and aprogressive cache 1730.

The pipeline 1710 includes rendering stages 1711–1716 connected seriallyto each other. The first stage 1711 receives as input a renderingrequest 1701, and the last stage 1716 outputs a display image 1702. Anoutput of each stage provides an input for a successive stage.

The cache manager 1720 connects the pipeline 1710 to the progressivecache 1730. The cache manager routes cache elements between the pipelineand the progressive cache.

The progressive cache 1730 includes a preprocessed shape descriptorcache 1731, a distance field cache 1732, a distance values cache 1733,an antialised intensities cache 1734, and a colorized image cache 1735.The progressive caches 1731–1735 are arranged, left-to-right in FIG. 17,from a least finished, i.e., least complete, cache element to a mostfinished, i.e., most complete, cache element, hence, the cache 1730 isdeemed to be ‘progressive’.

Each cache 1731–1735 includes a data store for input to a next stage ofa corresponding stage in the rendering pipeline 1710 and for output ofthe corresponding stage. The one-to-one correspondences between therendering stages of the pipeline and the data stores are indicatedgenerally by the dashed double arrows 1741–1745. The stages increase alevel of completion of elements passing through the pipeline, and thereis a cache for each level of completion.

Rendering Using a Progressive Cache—System Operation

First, the rendering request 1701 for a graphics object is generated.

Second, the progressive cache 1730 is queried 1721 by the cache manger1720 to determine a most complete cached element 1722 most representingthe display image 1702, e.g., elements of cache types 1–5, which isavailable to satisfy the rendering request.

Third, a result of querying the progressive cache, i.e., the mostcomplete cached element 1722, is sent, i.e., piped, to the appropriaterendering stage, i.e., the next stage of the corresponding stage of thecache containing the most complete cached element 1722, to complete therendering of the object. If no cache element is available 1723, thenprocessing of the rendering request commences in stage 1712.

After each rendering stage completes processing, the output of the stagecan also be sent, i.e., piped, back to the progressive cache 1730, viathe cache manger 1720, for potential caching and later reuse. Forexample, the output of stage 1716 is sent as input to the cache 1735.

Applying compression methods to cached elements in the progressive cache1730 increases the effective size of the progressive cache 1730, thusincreasing the overall efficiency of the pipeline 1710 by providing agreater cache hit ratio. The distance field cache 1732 and the distancevalues cache 1733 are particularly amenable to compression because ofthe continuous nature of distance fields.

There are numerous ways known in the art to store and locate cachedelements in the individual caches 1731–1735. One such method is hashing,where a key is constructed from the rendering request 1701 and thenhashed to produce an index indicating a location of a potentially cachedelement. When the rendering request 1701 comprises a glyph of aspecified typeface, the key could comprise a bitwise concatenation of acharacter code for the glyph and a name for the typeface.

To increase the effectiveness of our progressive cache 1730, we can usea least-recently-used, i.e., LRU, method for managing cached elements.In this method, least-recently-used cached elements are discarded whenthe progressive cache 1730 becomes full. It is important to note,however, that our progressive cache 1730 can use various memorymanagement methods for cached elements and is not limited to the LRUmethod.

In another embodiment of the system 1700, there are fewer caches in theprogressive cache 1730 than there are stages in the rendering pipeline1710. In this embodiment, not all stages have a corresponding cache. Itis sometimes advantageous to eliminate an individual cache in theprogressive cache 1730 because the corresponding stage is extremelyefficient and caching the output in the individual cache would beunnecessary and would waste memory. Furthermore, the output of thecorresponding stage may require too much memory to be practical.

One skilled in the art would readily understand how to adapt the system1700 to include various rendering pipelines and various progressivecaches to enable a rendering request to be satisfied.

Processing Pixel Components

A pixel comprises one or more components. For example, pixels on atypical CRT or LCD color monitor comprise a red, a green, and a bluecomponent. In our invention, when the pixel includes multiplecomponents, they can be treated independently, as described above, orprocessed as a single component. When the multiple components areprocessed as a single component, a color and an alpha value of the pixelcan be determined from the antialiased intensity of the singlecomponent.

There are two reasons to process the multiple components as a singlecomponent. First, it reduces rendering times. Second, when the multiplecomponents cannot be addressed individually or when the relativepositions of the individual components are not known, individualtreatment of each component is difficult.

When display devices, such as LCDs and OLEDs, have addressable pixelcomponents, it is known in the art that processing the multiplecomponents independently can increase the effective resolution of thedevice. Our invention can exploit this feature of such devices toprovide distance-based antialiasing with superior quality over the priorart.

When rendering on alternative pixel layouts with addressable pixelcomponents our invention has numerous advantages over the prior art. Forexample, we can use a single distance sample per pixel component andachieve superior quality over the prior art, even when the prior artuses several coverage-based samples per pixel component. Our methods areinherently fast enough on any layout and do not require reusing sampleslike the prior art. In the prior art, the reuse of samples fails to workon many alternative pixel layouts. Furthermore, by adjusting ourrendering parameters, such as the mapping 440 shown in FIG. 4, ourmethods mitigate the color fringing problems of the prior art and allowus to account for various characteristics of pixel components, such assize and brightness.

Animating Two-Dimensional Objects

FIG. 12 shows a flow diagram of a method 1200 for animating an object1201 as a sequence of frames according to an animation script 1202. Theanimation script 1202 directs conditions of the object, e.g., theposition, size, orientation, and deformation of the object, for eachframe in the sequence of frames. The object is represented as atwo-dimensional distance field. A pose 1211 of the object 1201 isupdated 1210 for each frame in the sequence of frames 1221 according tothe animation script 1202. The object 1201 is rendered using the updatedpose 1211 and a distance-based antialiasing rendering method 1212.

The two-dimensional distance field representing the object 1201 can beacquired from a different representation of the object, e.g., an outlinedescription of the object or a bitmap description of the object.

The updating 1210 of the pose 1211 for a particular object 1201 can beperformed by applying various operations to the object including a rigidbody transformation, a free-form deformation, a soft-body impactdeformation, a level-set method, a particle simulation, and a change toits rendering attributes.

When rendering 1220 the object, we associate a set of sample points inthe two-dimensional distance field representing the object with acomponent of a pixel in a frame in the sequence of frames 1221. Bydetermining a distance from the two-dimensional distance field and theset of sample points, we can map the distance to an antialiasedintensity of the component of the pixel.

In a preferred embodiment, we partition the two-dimensional distancefield representing the object 1201 into cells, each cell including amethod for reconstructing the two-dimensional distance field within thecell. To render 1220 in this instance, we identify a set of cells of thetwo-dimensional distance field representing the object 1201 thatcontains a region of the two-dimensional distance field to be renderedand locate a set of pixels associated with the region. A set ofcomponents for each pixel in the set of pixels is specified. A distancefor each component of the pixel is determined from the set of cells andthe distance is mapped to the antialiased intensity of the component ofthe pixel to determine an antialiased intensity for each component ofeach pixel in the set of pixels.

Distance-Based Automatic Hinting

Hinting in standard font representations is a time-consuming manualprocess in which a type designer and hinting specialist generate a setof rules for better fitting individual glyphs to the pixel grid. Goodhinting produces glyphs at small type sizes that are well spaced, havegood contrast, and are uniform in appearance.

These rules provide: vertical stems with the same contrast distribution,with the left and bottom edges having the sharpest possible contrast;diagonal bars and thin, rounded parts of glyphs to have sufficientcontrast for transmitting visual structure to the eye; and serifs thathold together and provide enough emphasis to be captured by the humaneye, see Hersch et al., “Perceptually Tuned Generation of GrayscaleFonts,” IEEE CG&A, November, pp. 78–89, 1995.

Note that prior art filtering methods produce fuzzy characters andassign different contrast profiles to different character parts, thusviolating important rules of type design. To overcome these limitations,hints are developed for each glyph of each font. There are numerousproblems with prior art hinting methods: they are labor intensive todevelop, slow to render, and complex thus precluding hardwareimplementations.

For outline-based fonts, rendering with hints is a three step process.First, the glyph's outlines are scaled and aligned to the pixel grid.Second, the outlines are modified to control contrast of stems, bars,and serifs and to increase the thickness of very thin sections and arcs.Third, the modified outlines are supersampled followed by down-samplingwith filtering.

Although our unhinted distance-based antialiasing rendering methodsdescribed above compare favorably with prior art font rendering methodsthat use hinting, it is known that perceptual hinting can improvereading comfort at small type sizes.

Therefore, as shown in FIG. 8, we exploit the distance field to providedistance-based automatic hinting 800 for rendering glyphs at small pointsizes. The first step 810 in hinting is to scale and align the distancefield to the pixel or pixel component grid. This can be doneautomatically from the given or derived font metrics, e.g., thecap-height, the x-height, and the position of the baseline. Font metricscan be derived automatically from the distance field by using a gradientof the distance field to detect specific font metrics, such as thecap-height. The step 810 can include a general transformation of thedistance field, e.g., a deformation, to enable a proper alignment to thepixel or pixel component grid.

After applying this form of grid fitting, we use the distance field andits gradient field to provide perceptual hints.

In one embodiment, the direction of the gradient of the distance fieldis used to detect 820 pixels on the left and bottom edges of the object.By darkening 830 these pixels and lightening 840 pixels on oppositeedges, we achieve higher contrast on left and bottom edges withoutchanging the apparent stroke weight. This can be done by decreasing andincreasing the corresponding pixel intensities.

In another embodiment, the gradient field is used to provide bettercontrast for diagonal stems and thin arcs. We note that when a pixel islocated on or near thin regions of the glyph, neighbors on either sideof the pixel have opposite gradient directions, i.e., their dot productsare negative. By detecting abrupt changes in gradient directions, we candarken 850 pixels on these thin regions.

These are only two examples of how the distance field can be used toprovide perceptual hints automatically. The distance field can also beused to provide optimal character spacing and uniform stroke weight.

Typesetting Glyphs

Typesetting determines positions of glyphs given input data such as alayout, a starting position of the layout, and associated font metricsfor the glyphs such as set-widths and kerning pairs. We define anescapement of a glyph as an offset, e.g., a vector, to a next glyph; theescapement typically includes a set-width of the glyph, the set-widthand a kerning value, or numerous other combinations specified by a user,dictated by the layout, or derived from the font metrics. The escapementtakes into consideration typesetting on lines, Bezier curves, or othercomplex paths specified by the layout. “TEX and METAFONT: New Directionsin Typesetting” provides a good overview of typesetting.

Typical applications of typesetting include determining positions ofletters in a word and determining line-breaks of a paragraph.Typesetting considers the underlying representation of the glyphs whendetermining their positions. For example, bitmap fonts cannot bepositioned to a fraction of a pixel, whereas outline fonts can. Outlinefonts are often hinted, which results in adjustments to the positions ofthe glyphs.

Typesetting Glyphs Represented as Two-Dimensional Distance Fields

There are numerous ways to typeset glyphs represented as two-dimensionaldistance fields.

In one embodiment, we turn off distance-based automatic hinting toenable an exact placement of glyph positions as dictated by atypesetting method.

In another embodiment, we use distance-based automatic hinting to gridfit, i.e., align, a distance field representing each glyph to a pixelgrid, thus approximating the placement of glyph positions, as dictatedby the typesetting method, to a fraction of a pixel.

In another embodiment, to achieve greater accuracy, we usedistance-based automatic hinting to grid fit, i.e., align, a distancefield representing each glyph to a component of a pixel grid, thusapproximating the placement of glyph positions, as dictated by thetypesetting method, to an even smaller fraction of a pixel.

In another embodiment, as shown in FIGS. 18A–18C, a method 1800 typesetsa set of glyphs 1801. The set of glyphs 1801 can represent, for example,letters of a word, or letters of a document. A current glyph 1802 isselected 1805 from the set of glyphs 1801, e.g., a first letter of theword is selected. A current position 1803 is also selected 1810. Theselection 1810 can be chosen by a user with an input device such as amouse or derived from a layout for the set of glyphs 1801.

A termination condition 1804 is tested 1815, e.g., are all letters ofthe word typeset, and if satisfied, the method 1800 halts. If thetermination condition 1804 is not satisfied 1850, then the method 1800iterates to determine a next position 1809 of a next glyph 1806, e.g., anext letter in the word, where the next glyph 1806 is selected 1820 fromthe set of glyphs 1801.

After the selection 1820, the current glyph 1802 is represented 1825 asa two-dimensional distance field 1807. Then, the next position 1809 isdetermined 1830 using the current position 1803, an escapement 1808 ofthe current glyph 1802, and an alignment 1835 of the two-dimensionaldistance field 1807, e.g., the next position 1809 is determined as anoffset of the escapement 1808 from the current position 1803 where theoffset is adjusted accordingly to the alignment 1835.

Finally, the current glyph 1802 is updated 1840 to be the next glyph1806 and the current position 1803 is updated 1845 to be the nextposition 1809 to prepare for the next iteration.

The alignment 1835 can be a consequence of a rendering of the currentglyph 1802 or can be determined without rendering. Note that thealignment 1835 can depend on a selected iso-contour of thetwo-dimensional distance field 1807 because the selected iso-contour canchange a size of the current glyph 1802.

In another embodiment, the next position 1809 is determined 1830 usingthe current position 1803, an escapement 1808 of the current glyph 1802,and a selected iso-contour of the two-dimensional distance field 1807.For example, the next position 1809 can be determined as an offset ofthe escapement 1808 from the current position 1803, where the offset isadjusted accordingly to the selected iso-contour.

A zero iso-contour may result in no adjustment. A negative iso-contourmay result in a larger offset from the current position 1803 because thenegative iso-contour increases a size of the current glyph 1802. Apositive iso-contour may result in a smaller offset from the currentposition 1803 because the positive iso-contour decreases the size of thecurrent glyph 1802.

Generating and Editing Fonts

There are two basic methods for designing fonts. The first is manual.There, glyphs are drawn by hand, digitized, and then outlines are fit tothe digitized bitmaps. The second is by computer.

In the latter case, three types of tools are available. Direct visualtools can be used for curve manipulation. Procedural design toolsconstruct the shape of a glyph by executing the instructions of aprocedure. The procedure defines either a shape's outline and fills it,or defines a path stroked by a pen nib with numerous attributes,including a geometry and an orientation. Component-based design toolsallow designers to build basic components such as stems, arcs, and otherrecurring shapes, and then combine the components to generate glyphs.

We use a sculpting editor to provide stroke-based design. This is the 2Dcounterpart to 3D carving as described in U.S. patent application Ser.No. 09/810,261, “System and Method for Sculpting Digital Models,” filedon Mar. 16, 2001, incorporated herein by reference. Stroking can be doneinteractively or it can be scripted to emulate programmable designtools.

Curve-based design, using Bezier curve manipulation tools similar tothose in Adobe Illustrator can also be used. Curve-based design can becombined with methods for converting outlines to distance fields anddistance fields to outlines to provide a seamless interface betweendesign paradigms.

Component-based design uses CSG and blending operations on the implicitdistance field. This allows components to be designed separately andcombined either during editing or during rendering.

We also provide a method for automatically generating ADFs from analogand digital font masters.

For component-based design, our font editor provides the ability toefficiently reflect and rotate ADFs using quadtree manipulation to modelthe symmetries common in glyphs. Additional features include ADFscaling, translation, and operations to combine multiple ADFs, e.g., CSGand blending.

For stroke-based design, we provide carving tools with a geometricprofile to emulate pen nibs. The orientation and size of the simulatedpen nib can change along the stroke to mimic calligraphy.

FIG. 9 shows a method 900 for generating a two-dimensional distancefield 931 from a pen stroke. We sample a pen state during a pen stroke,the pen state comprising a location of the pen during the stroke. Thispen state may also include orientation and geometry. From the pen statesamples 901, we generate 910 an ordered list 911 of pen states along thepen stroke. Then, a set of boundary descriptors 921 is generated 920from the ordered list of pen states. Finally, we generate 930 atwo-dimensional distance field 931 from the set of boundary descriptors921.

In the preferred embodiment, the boundary descriptors 921 are curvessuch as cubic Bezier curves.

In the preferred embodiment, we apply a curve fitting process to fit aminimum set of G² continuous curves to the path of the pen, withuser-specified accuracy. We also generate two additional ordered listsof offset points from this path using the tool size and orientation, andfit curves to these offset points to generate the stroke outlines. Theoutline curves are placed in a spatial hierarchy for efficientprocessing. We generate a two-dimensional ADF from this hierarchy usinga tiled generator, see U.S. Pat. application Ser. No. 09/810,983, filedon Mar. 16, 2001, and incorporated herein by reference.

The minimum distance to the outlines is computed efficiently usingBezier clipping. Strokes are converted to ADFs without a perceptualdelay for the user. For curve manipulation, we provide a Bezier curveeditor.

As shown in FIG. 11, we also provide the ability to convert distancefields to boundary descriptors, e.g., Bezier curves, to provide aseamless interface between all three design paradigms.

In the preferred embodiment, we use bi-quadratic ADFs where thisconversion traverses the leaf cells using the ADF hierarchy for fastneighbor searching, generates an ordered list of points along thezero-valued iso-contours of the ADF, and then fits curves as describedwith reference to FIG. 11, below, to generate the boundary descriptors.

In contrast with the prior art, where boundary descriptor errors arecomputed from the list of points, we compute the boundary descriptorerror directly from the distance field. We pay special attention tosharp corners. Our approach is fast enough to allow users to seamlesslyswitch between paradigms without any noticeable delay.

FIG. 11 shows a method 1100 for converting a two-dimensional distancefield 1101 to a set of boundary descriptors 1131. First, we select 1110an iso-contour 1111 of the two-dimensional distance field 1101, e.g.,distances with a zero value, or some offset.

Next, we generate 1120 an ordered list of points 1121 from theiso-contour 1111 and the two-dimensional distance field 1101. In ourpreferred embodiment using bi-quadratic adaptively sampled distancefields, this step visits neighboring cells of the adaptively sampleddistance field 1101 sequentially using a neighbor searching technique.The search technique exploits a spatial hierarchy of the adaptivelysampled distance field 1101 to efficiently localize a next neighboralong the iso-contour 1111.

In another embodiment, we generate 1120 an ordered list of points 1121by selecting boundary cells in the ADF 1101, seeding each boundary cellwith a set of ordered points, and moving each point to the iso-contour1111 of the ADF 1101 using a distance field and a gradient field of theADF 1101.

Then, we initialize 1130 a set of boundary descriptors 1131 to fit theordered list of points 1121. The boundary descriptors 1131 areinitialized 1130 by joining adjacent points of the ordered list ofpoints 1121 to form a set of line segments that constitute the initialboundary descriptors 1131.

In another embodiment, we initialize 1130 a set of boundary descriptors1131 by locating corner points, subdividing the ordered list of pointsinto segments delimited by the corner points, and determining segmentboundary descriptors to fit each segment. The union of the segmentboundary descriptors forms the initial boundary descriptors 1131.

Corner points can be located by measuring curvature determined from thedistance field. In the preferred embodiment, where the distance field isa bi-quadratic ADF, regions of high curvature are represented by smallcells in the ADF and hence corner points can be located by using ADFcell sizes.

Once the boundary descriptors 1131 are initialized 1130, the boundarydescriptors 1131 are updated 1140. The updating 1140 determines an errorfor each boundary descriptor by reconstructing the distance field andmeasuring the average or maximum deviation of the boundary descriptorfrom the iso-contour.

The boundary descriptors 1131 are updated 1140 until the error for eachboundary descriptor is acceptable, or a predetermined amount of time haselapsed, or a cardinality of the set of boundary descriptors 1131 isminimal.

To incorporate the existing legacy of fonts stored in non-digital form,i.e., as analog masters, or in digital form as bitmaps, i.e., as digitalmasters, our editing system provides a method for generating ADFs fromhigh-resolution bi-level bitmaps.

Analog masters are first scanned to produce bi-level digital masters ata resolution at least four times higher than the target ADF resolution,e.g., a 4096×4096 digital master is adequate for today's displayresolutions and display sizes. An exact Euclidean distance transform isthen applied to the bitmap to generate a regularly sampled distancefield representing the glyph.

Then, we generate an ADF from this regularly sampled distance fieldusing the tiled generator. Conversion from the bitmap to the ADFrequires ˜10 seconds per glyph on a 2 GHz Pentium IV processor.

To convert from existing prior art descriptors of glyphs to distancefields where the glyphs are described with a set of boundarydescriptors, we apply the method described with reference to FIG. 10.

Generating and Rendering Component-Based Glyphs

The present invention provides methods for generating and rendering acomposite glyph. Unlike prior art methods, which represent components,i.e., elements, by outline descriptors or stroked skeletons and eithercombine the elements into a single shape descriptor prior to renderingor rasterize each element and combine antialiased intensities orcoverage values, the present invention represents elements of thecomposite glyph as two-dimensional distance fields and renders thecomposite glyph using these two-dimensional distance fields.

In a preferred embodiment, the rendering combines distances determinedfor a component of a pixel using the two-dimensional distance fields andthen maps a combined distance to an antialiased intensity for thecomponent of the pixel. By combining distance values rather thanantialiased intensities or coverage values, the present inventionmitigates color artifacts and blending artifacts exhibited by the priorart.

Unlike the prior methods of Perry et al., the present invention does notgenerate a combined distance field to represent the composite glyphprior to rendering. Instead, according to our invention, the combineddistance associated with the component of the pixel is determinedon-demand during rendering by combining distances determined from eachelement.

FIGS. 19A and 19B show a method 1900 for generating a composite glyph1911 and rendering a region 1941 of the composite glyph 1911 in imageorder, producing a rendered region 1943. The composite glyph 1911 isfirst defined 1910 by a set of elements 1901. A set of two-dimensionaldistance fields 1930 is then generated 1920 using the set of elements1901 such that the composite glyph 1911 is represented by a compositionof distance fields 1931–1933 in the set of two-dimensional distancefields 1930. The region 1941 of the composite glyph 1911 is rendered1940 using the set of two-dimensional distance fields 1930.

FIG. 19C shows a preferred embodiment for the rendering 1940 of themethod 1900. Each pixel 1944 in the region 1941 can include one or morecomponents 1946, typically a red, green, and blue component for RGBrendering. The rendering 1940 determines, for each component 1946 ofeach pixel 1944 in the region 1941, an antialiased intensity 1942.

Sets of sample points 1951–1953 are associated 1950 with the pixelcomponent 1946, there being a one-to-one correspondence between each setof sample points and each distance field in the set of two-dimensionaldistance fields 1930. For example, the set of sample points 1951corresponds to the distance field 1931 and the set of sample points 1953corresponds to the distance field 1933.

A corresponding distance is then determined 1960 for each distance field1931–1933 using its corresponding set of sample points 1951–1953,producing corresponding distances 1961–1963. For example, thecorresponding distance 1961 is determined 1960 for the distance field1931 using its corresponding set of sample points 1951.

The corresponding distances 1961–1963 are then combined 1970 todetermine a combined distance 1971. The combined distance 1971 is thenmapped 1980 to determine the antialiased intensity 1942 of the component1946 of the pixel 1944.

FIGS. 20A and 20B show a method 2000 for generating a composite glyph2006 and rendering a region 2036 of the composite glyph 2006 in objectorder, producing a rendered region 2037. The composite glyph 2006 isfirst defined 2005 by a set of elements 2001. A set of two-dimensionaldistance fields 2020 is then generated 2010 using the set of elements2001 such that the composite glyph 2006 is represented by a compositionof distance fields 2021–2023 in the set of two-dimensional distancefields 2020.

Each distance field 2021–2023 in the set of two-dimensional distancefields 2020 is partitioned 2025 into cells, where each cell isassociated 2030 with a method for reconstructing 2031 thetwo-dimensional distance field within the cell. The region 2036 of thecomposite glyph 2006 is then rendered 2035 using the set oftwo-dimensional distance fields 2020.

FIGS. 20C and 20D show a preferred embodiment for the rendering 2035 ofthe method 2000. To render the region 2036 of the composite glyph 2006,a set of pixels 2046 is located 2045 from the region 2036 and a set ofcomponents 2055 for each pixel in the set of pixels 2046 is specified2050. Note that each pixel in the set of pixels 2046 can include one ormore components, typically a red, green, and blue component for RGBrendering. The rendering 2035 determines an antialiased intensity 2061for each component 2056 of each pixel in the set of pixels 2046.

For each two-dimensional distance field 2021–2023 in the set oftwo-dimensional distance fields 2020 shown in FIG. 20B, a correspondingset of cells 2041–2043 associated with the region 2036 is identified2040, e.g., the set of cells 2041 is identified 2040 for the distancefield 2021 and the set of cells 2043 is identified 2040 for the distancefield 2023.

For each component 2056 of each pixel in the set of pixels 2046, anantialiased intensity 2061 is determined 2060 by first determining 2070,for the component 2056, a corresponding distance 2071-2073 for eachdistance field 2021–2023 using the corresponding set of cells 2041–2043.For example, the corresponding distance 2071 is determined 2070 for thecomponent 2056 for the distance field 2021 using the set of cells 2041.

The corresponding distances 2071–2073 are then combined 2075 todetermine a combined distance 2076. The combined distance 2076 is thenmapped 2080 to produce the antialiased intensity 2061 of the component2056 of the pixel.

The elements 1901 of the composite glyph 1911 of the method 1900 and theelements 2001 of the composite glyph 2006 of the method 2000 can havemany representations. For example, they can be represented byone-dimensional and two-dimensional shape descriptors such as strokes,outlines, radicals, stroked radicals, paths, and user-drawn curves,strokes, and paths. An element can be represented by a distance fieldsuch as a distance map, an adaptively sampled distance field, aprocedure for generating distance and a distance function. An elementitself can be a composition such as an implicit blend of a first shapedescriptor and a second shape descriptor or a skeleton with an offsetdescriptor.

The elements 1901 can be defined 1910 and the elements 2001 can bedefined 2005 using a number of approaches. For example, the defining canbe performed automatically using a procedure such as automatic shapedetection, shape matching, and skeletonization. The defining can beperformed interactively by a user or semi-automatically with a userguiding a procedure for defining the elements.

The defining 1910 and 2005 can be performed from a distance fieldrepresenting the composite glyph. For example, the elements can bedefined by performing distance-based automatic shape detection, shapematching, and skeletonization on the distance field. In addition, thedefining can first determine a shape descriptor for an element and thendetermine a distance function for the shape descriptor to define theelement.

A distance field in the sets of two-dimensional distance fields 1930 and2020 can be represented as an adaptively sampled distance field, a setof distances stored in memory, or by a procedure, to name but a few.

Several approaches can be used for combining 1970 the correspondingdistances 1961–1963 in the method 1900 and for combining 2075 thecorresponding distances 2071–2073 in the method 2000. For example, usinga positive-inside, negative-outside sign convention for the distancefields, the combining can take a maximum of the corresponding distancesto produce a union of the objects or a minimum of the correspondingdistances to produce an intersection of the objects.

Other combining methods include taking a difference, performing anarithmetic average, or performing an implicit blend of the correspondingdistances, to name but a few. An implicit blend can be used to roundcorners between the objects while an arithmetic average can be used toprovide additional antialiasing by further reducing high frequencycontent in the rendered region. More generally, the combining can be anyarithmetic or conditional operation. Furthermore, the combining can usea procedure or a table to determine the combined distance.

Computational Substrate for Kinetic Typography

The distance field and the spatial hierarchy attributes of our ADF glyphframework can also be used for computer simulation of 2D objects, e.g.,glyphs, corporate logos, or any 2D shape. For example, both attributescan be used in collision detection and avoidance, for computing forcesbetween interpenetrating bodies, and for modeling soft body deformation.

Level set methods, which use signed distance fields, can be used tomodel numerous effects such as melting and fluid dynamics. ADFs are acompact implicit representation that can be efficiently queried tocompute distance values and gradients, two important computationsrequired for the methods listed above.

In contrast, determining distance values and gradients from outlinesthat are moving or deforming is impractical in software for real-timeinteraction, see Hoff et al., “Fast and Simple 2D Geometric ProximityQueries Using Graphics Hardware,” Proc. Interactive 3D Graphics '01,2001. Hoff et al. use graphics hardware to generate a regularly sampled2D distance field on the fly for deforming curves approximated by linesegments.

The implicit nature of the distance field permits complex topologicalchanges, such as surface offsets that would be difficult to model withoutline-based fonts. In addition, distance fields can be used to providenon-photorealistic rendering of an animated object to add artisticeffect.

Effect of the Invention

The invention provides a novel framework for representing, rendering,editing, processing, and animating character glyphs, corporate logos, orany two-dimensional object.

In a preferred embodiment, the invention uses distance fields torepresent two-dimensional objects. The invention includes methods forgenerating various instantiations of distance fields, includingbi-quadratic ADFs and ADFs with specialized cells. Our methods provide asignificant reduction in memory requirements and a significantimprovement in accuracy over the prior art.

Our distance-based antialiasing rendering methods provide better andmore efficient antialiasing than the methods used in the prior art.

Our methods also provide a computational substrate for distance-basedautomatic hinting, for distance-based grid fitting, for generating andrendering stroke-based and radical-based composite glyphs, fortypesetting glyphs, for unifying three common digital font designparadigms, and for generating a variety of special effects for kinetictypography.

Our framework provides numerous advantages: highly legible type even atvery small font sizes without the use of labor intensive manual hinting;unparalleled adaptability for flat panel display technologies, such asOLEDs, with numerous and sometimes complex arrangements for thecomponents of a pixel; unique control of rendering parameters thatenable interactive user tuning of type for enhanced viewing comfort andpersonal preference; a computationally clean rendering pipelinestraightforward to implement in silicon and to implement on bothfixed-function graphics hardware and programmable graphics hardware; andsupport for advanced applications such as pen-based input.

Although the invention has been described by way of examples ofpreferred embodiments, it is to be understood that various otheradaptations and modifications can be made within the spirit and scope ofthe invention. Therefore, it is the object of the appended claims tocover all such variations and modifications as come within the truespirit and scope of the invention.

1. A method for rendering a region of a composite glyph, comprising:defining a composite glyph by a set of elements; generating a set oftwo-dimensional distance fields using the set of elements, wherein eachtwo-dimensional distance field in the set of two-dimensional distancefields is partitioned into cells, each cell including a method forreconstructing the corresponding two-dimensional distance field withinthe cell, a composition of the set of two-dimensional distance fieldsrepresenting the composite glyph; and rendering a region of thecomposite glyph using the set of two-dimensional distance fields, therendering further comprising: identifying, for each two-dimensionaldistance field in the set of two-dimensional distance fields, a set ofcells of the two-dimensional distance field, the set of cells associatedwith the region of the composite glyph; locating a set of pixelsassociated with the region; specifying a set of components for eachpixel in the set of pixels; and determining an antialiased intensity foreach component of each pixel in the set of pixels, the determiningfurther comprising: determining, for each two-dimensional distance fieldin the set of two-dimensional distance fields, a corresponding distancefor the component of the pixel from the corresponding set of cells;combining the corresponding distances to determine a combined distance;and mapping the combined distance to the antialiased intensity of thecomponent of the pixel.
 2. The method of claim 1 wherein a particularelement in the set of elements is a stroke.
 3. The method of claim 1wherein a particular element in the set of elements is an outline. 4.The method of claim 1 wherein a particular element in the set ofelements is a radical.
 5. The method of claim 1 wherein a particularelement in the set of elements is a stroked radical.
 6. The method ofclaim 1 wherein a particular element in the set of elements is atwo-dimensional shape descriptor.
 7. The method of claim 1 wherein aparticular element in the set of elements is a one-dimensional shapedescriptor.
 8. The method of claim 1 wherein a particular element in theset of elements is a path.
 9. The method of claim 1 wherein a particularelement in the set of elements is a distance field.
 10. The method ofclaim 1 wherein a particular element in the set of elements is adistance map.
 11. The method of claim 1 wherein a particular element inthe set of elements is an adaptively sampled distance field.
 12. Themethod of claim 1 wherein a particular element in the set of elements isa procedure.
 13. The method of claim 1 wherein a particular element inthe set of elements is a distance function.
 14. The method of claim 1wherein a particular element in the set of elements is an implicit blendof a first shape descriptor and a second shape descriptor.
 15. Themethod of claim 1 wherein a particular element in the set of elements isa skeletal descriptor with a corresponding offset descriptor.
 16. Themethod of claim 1 wherein a particular element in the set of elements isdrawn by a user.
 17. The method of claim 1 wherein the defining isperformed automatically by a procedure.
 18. The method of claim 1wherein the defining is performed by a user.
 19. The method of claim 1wherein the defining is performed semi-automatically by a procedure anda user.
 20. The method of claim 1 wherein the defining furthercomprises: determining a shape descriptor for a particular element inthe set of elements; and determining a distance function for the shapedescriptor to define the particular element.
 21. The method of claim 1wherein the defining determines the set of elements from a distancefield of a shape descriptor for the composite glyph.
 22. The method ofclaim 1 wherein a particular two-dimensional distance field in the setof two-dimensional distance fields is an adaptively sampled distancefield.
 23. The method of claim 1 wherein a particular two-dimensionaldistance field in the set of two-dimensional distance fields comprises aset of distances stored in a memory.
 24. The method of claim 1 wherein aparticular two-dimensional distance field in the set of two-dimensionaldistance fields is represented by a procedure.
 25. The method of claim 1wherein the combining performs a maximum of the corresponding distancesto determine the combined distance.
 26. The method of claim 1 whereinthe combining performs an arithmetic average of the correspondingdistances to determine the combined distance.
 27. The method of claim 1wherein the combining performs a union of the corresponding distances todetermine the combined distance.
 28. The method of claim 1 wherein thecombining performs an intersection of the corresponding distances todetermine the combined distance.
 29. The method of claim 1 wherein thecombining performs a difference of the corresponding distances todetermine the combined distance.
 30. The method of claim 1 wherein thecombining performs an implicit blend of the corresponding distances todetermine the combined distance.
 31. The method of claim 1 wherein thecombining performs an arithmetic operation on the correspondingdistances to determine the combined distance.
 32. The method of claim 1wherein the combining performs a conditional operation on thecorresponding distances to determine the combined distance.
 33. Themethod of claim 1 wherein the combining uses a procedure to determinethe combined distance.
 34. The method of claim 1 wherein the combininguses a table to determine the combined distance.
 35. A method forrendering a region of a composite glyph, comprising: defining acomposite glyph by a set of elements; generating a set oftwo-dimensional distance fields using the set of elements, wherein eachtwo-dimensional distance field in the set of two-dimensional distancefields is partitioned into cells, each cell including a method forreconstructing the corresponding two-dimensional distance field withinthe cell, a composition of the set of two-dimensional distance fieldsrepresenting the composite glyph; and rendering a region of thecomposite glyph using the set of two-dimensional distance fields. 36.The method of claim 35 wherein a particular element in the set ofelements is a stroke.
 37. The method of claim 35 wherein a particularelement in the set of elements is an outline.
 38. The method of claim 35wherein a particular element in the set of elements is a radical. 39.The method of claim 35 wherein a particular element in the set ofelements is a stroked radical.
 40. The method of claim 35 wherein aparticular element in the set of elements is a two-dimensional shapedescriptor.
 41. The method of claim 35 wherein a particular element inthe set of elements is a one-dimensional shape descriptor.
 42. Themethod of claim 35 wherein a particular element in the set of elementsis a path.
 43. The method of claim 35 wherein a particular element inthe set of elements is a distance field.
 44. The method of claim 35wherein a particular element in the set of elements is a distance map.45. The method of claim 35 wherein a particular element in the set ofelements is an adaptively sampled distance field.
 46. The method ofclaim 35 wherein a particular element in the set of elements is aprocedure.
 47. The method of claim 35 wherein a particular element inthe set of elements is a distance function.
 48. The method of claim 35wherein a particular element in the set of elements is an implicit blendof a first shape descriptor and a second shape descriptor.
 49. Themethod of claim 35 wherein a particular element in the set of elementsis a skeletal descriptor with a corresponding offset descriptor.
 50. Themethod of claim 35 wherein a particular element in the set of elementsis drawn by a user.
 51. The method of claim 35 wherein the defining isperformed automatically by a procedure.
 52. The method of claim 35wherein the defining is performed by a user.
 53. The method of claim 35wherein the defining is performed semi-automatically by a procedure anda user.
 54. The method of claim 35 wherein the defining furthercomprises: determining a shape descriptor for a particular element inthe set of elements; and determining a distance function for the shapedescriptor to define the particular element.
 55. The method of claim 35wherein the defining determines the set of elements from a distancefield of a shape descriptor for the composite glyph.
 56. The method ofclaim 35 wherein a particular two-dimensional distance field in the setof two-dimensional distance fields is an adaptively sampled distancefield.
 57. The method of claim 35 wherein a particular two-dimensionaldistance field in the set of two-dimensional distance fields comprises aset of distances stored in a memory.
 58. The method of claim 35 whereina particular two-dimensional distance field in the set oftwo-dimensional distance fields is represented by a procedure.
 59. Themethod of claim 35 wherein the rendering further comprises: identifying,for each two-dimensional distance field in the set of two-dimensionaldistance fields, a set of cells of the two-dimensional distance field,the set of cells associated with the region of the composite glyph;locating a set of pixels associated with the region; specifying a set ofcomponents for each pixel in the set of pixels; and determining anantialiased intensity for each component of each pixel in the set ofpixels.
 60. The method of claim 59 wherein the determining furthercomprises: determining, for each two-dimensional distance field in theset of two-dimensional distance fields, a corresponding distance for thecomponent of the pixel from the corresponding set of cells; combiningthe corresponding distances to determine a combined distance; andmapping the combined distance to the antialiased intensity of thecomponent of the pixel.
 61. The method of claim 60 wherein the combiningperforms a maximum of the corresponding distances to determine thecombined distance.
 62. The method of claim 60 wherein the combiningperforms an arithmetic average of the corresponding distances todetermine the combined distance.
 63. The method of claim 60 wherein thecombining performs a union of the corresponding distances to determinethe combined distance.
 64. The method of claim 60 wherein the combiningperforms an intersection of the corresponding distances to determine thecombined distance.
 65. The method of claim 60 wherein the combiningperforms a difference of the corresponding distances to determine thecombined distance.
 66. The method of claim 60 wherein the combiningperforms an implicit blend of the corresponding distances to determinethe combined distance.
 67. The method of claim 60 wherein the combiningperforms an arithmetic operation on the corresponding distances todetermine the combined distance.
 68. The method of claim 60 wherein thecombining performs a conditional operation on the correspondingdistances to determine the combined distance.
 69. The method of claim 60wherein the combining uses a procedure to determine the combineddistance.
 70. The method of claim 60 wherein the combining uses a tableto determine the combined distance.